Homework question...need help (College Algebra)

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alldogs

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Not sure if anyone knows how to figure this out but looked everywhere in the book for examples and received none. I've done #1 and just did a scatter plot in excel.

Market Research
A local grocery store has agreed to sell your homemade bread. You will use the following information along with some ideas from Chapter 3 to decide how many loaves should be manufactured each week and what price should be charged.
After tracking weekly sales at several different prices, you get the following data:
<TABLE style="BORDER-BOTTOM: medium none; BORDER-LEFT: medium none; BORDER-COLLAPSE: collapse; BORDER-TOP: medium none; BORDER-RIGHT: medium none" border=1 cellSpacing=0 cellPadding=0><TBODY><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>Loaves Sold, x
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>Price, p
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
347​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$1.50​
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
330​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$2.00​
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
293​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$2.50​
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
245​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$3.00​
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
223​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$3.50​
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
177​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$4.00​
</TD></TR></TBODY></TABLE>​
In order to increase manufacturing capacity, you’ve taken out a loan to buy an industrial sized oven for $3500. The new oven will allow you to make a maximum of about 400 loaves of bread per week. The loan is to be paid back monthly over two years at an annual interest rate of 10% compounded monthly. The monthly payments are $177.97. (You can check these numbers after section 5.7.) The ingredients for two loaves of bread are given in the table below. The $1.182 is the cost of the ingredients for a single loaf of bread.

<TABLE style="BORDER-BOTTOM: medium none; BORDER-LEFT: medium none; WIDTH: 4.25in; BORDER-COLLAPSE: collapse; BORDER-TOP: medium none; BORDER-RIGHT: medium none" border=1 cellSpacing=0 cellPadding=0 width=408><TBODY><TR style="HEIGHT: 17.5pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 17.5pt; BORDER-TOP: black 1pt solid; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>ingredients
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 17.5pt; BORDER-TOP: black 1pt solid; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>price/package size
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 17.5pt; BORDER-TOP: black 1pt solid; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>price / single loaf
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>5 cups flour
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$3.86 / 19 cups
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.508
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>3 Tbs. sugar
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$4.98 / 378 Tbs.
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.020
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>2 tsp. salt
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.52 / 122 ¾ tsp.
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.004
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>¼ tsp. baking soda
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.60 / 100 ¾ tsp.
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.001
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>1 package dry yeast
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.66 / package
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.330
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>1 cup buttermilk
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$1.17 / 4 cups
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.146
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>1/3 cup milk
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$2.38 / gallon
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.025
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>1 egg
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$2.35 / dozen
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.098
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>packaging
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.050
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>Total
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$1.182
</TD></TR></TBODY></TABLE>
  • Demand Equation. Make a scatter plot of the six data points (using the number sold as the x-coordinate.) Does the relationship appear to be linear? Use regression analysis to find the line of best fit. This line will be your demand equation. How strong is the correlation?
  • Revenue Function. Find R(x), the weekly revenue as a function of loaves sold, x. (Note that R(x) is an equation not a single value.)
  • Cost Function. Find C(x), the weekly cost for producing x loaves of bread. Be sure to include both the cost of the oven and the ingredients. What is the domain of the cost function?
  • Profit Function. Find P(x), the weekly profit for producing and selling x loaves of bread. (Hint: profit = revenue – cost.)
  • Maximum Revenue. Find the number of loaves that should be sold in order to maximize revenue. What is the maximum revenue? What price should be charged in order to maximize revenue?
  • Maximum Profit. Find the number of loaves that should be produced and sold in order to maximize the profit. What is the maximum profit? What price should be used to maximize profit?
  • Conclusion. How many loaves of bread will you produce each week and how much will you charge for each loaf? Why?
Can't tell anyone thanks enough if they can help.
 
wilheim

wilheim

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Moved to Financial Investment Forum from Offshore Forum for assistance.



Thank you, wilheiml.
 

OnWisconsin

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alldogs said:
Not sure if anyone knows how to figure this out but looked everywhere in the book for examples and received none. I've done #1 and just did a scatter plot in excel.

Market Research
A local grocery store has agreed to sell your homemade bread. You will use the following information along with some ideas from Chapter 3 to decide how many loaves should be manufactured each week and what price should be charged.
After tracking weekly sales at several different prices, you get the following data:
<TABLE style="BORDER-BOTTOM: medium none; BORDER-LEFT: medium none; BORDER-COLLAPSE: collapse; BORDER-TOP: medium none; BORDER-RIGHT: medium none" border=1 cellSpacing=0 cellPadding=0><TBODY><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>Loaves Sold, x
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: black 1pt solid; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>Price, p
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
347​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$1.50​
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
330​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$2.00​
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
293​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$2.50​
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
245​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$3.00​
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
223​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$3.50​
</TD></TR><TR><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
177​
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=bottom>
$4.00​
</TD></TR></TBODY></TABLE>​
In order to increase manufacturing capacity, you’ve taken out a loan to buy an industrial sized oven for $3500. The new oven will allow you to make a maximum of about 400 loaves of bread per week. The loan is to be paid back monthly over two years at an annual interest rate of 10% compounded monthly. The monthly payments are $177.97. (You can check these numbers after section 5.7.) The ingredients for two loaves of bread are given in the table below. The $1.182 is the cost of the ingredients for a single loaf of bread.

<TABLE style="BORDER-BOTTOM: medium none; BORDER-LEFT: medium none; WIDTH: 4.25in; BORDER-COLLAPSE: collapse; BORDER-TOP: medium none; BORDER-RIGHT: medium none" border=1 cellSpacing=0 cellPadding=0 width=408><TBODY><TR style="HEIGHT: 17.5pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 17.5pt; BORDER-TOP: black 1pt solid; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>ingredients
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 17.5pt; BORDER-TOP: black 1pt solid; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>price/package size
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 17.5pt; BORDER-TOP: black 1pt solid; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>price / single loaf
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>5 cups flour
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$3.86 / 19 cups
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.508
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>3 Tbs. sugar
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$4.98 / 378 Tbs.
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.020
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>2 tsp. salt
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.52 / 122 ¾ tsp.
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.004
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>¼ tsp. baking soda
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.60 / 100 ¾ tsp.
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.001
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>1 package dry yeast
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.66 / package
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.330
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>1 cup buttermilk
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$1.17 / 4 cups
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.146
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>1/3 cup milk
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$2.38 / gallon
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.025
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>1 egg
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$2.35 / dozen
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.098
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>packaging
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$0.050
</TD></TR><TR style="HEIGHT: 9pt"><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: black 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>Total
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>
</TD><TD style="BORDER-BOTTOM: black 1pt solid; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 5.4pt; PADDING-RIGHT: 5.4pt; HEIGHT: 9pt; BORDER-TOP: medium none; BORDER-RIGHT: black 1pt solid; PADDING-TOP: 0in" vAlign=top>$1.182
</TD></TR></TBODY></TABLE>
  • Demand Equation. Make a scatter plot of the six data points (using the number sold as the x-coordinate.) Does the relationship appear to be linear? Use regression analysis to find the line of best fit. This line will be your demand equation. How strong is the correlation?
  • Revenue Function. Find R(x), the weekly revenue as a function of loaves sold, x. (Note that R(x) is an equation not a single value.)
  • Cost Function. Find C(x), the weekly cost for producing x loaves of bread. Be sure to include both the cost of the oven and the ingredients. What is the domain of the cost function?
  • Profit Function. Find P(x), the weekly profit for producing and selling x loaves of bread. (Hint: profit = revenue – cost.)
  • Maximum Revenue. Find the number of loaves that should be sold in order to maximize revenue. What is the maximum revenue? What price should be charged in order to maximize revenue?
  • Maximum Profit. Find the number of loaves that should be produced and sold in order to maximize the profit. What is the maximum profit? What price should be used to maximize profit?
  • Conclusion. How many loaves of bread will you produce each week and how much will you charge for each loaf? Why?
Can't tell anyone thanks enough if they can help.
Click to expand...

:think2::think2:

hope that helps
 
cincy_

cincy_

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Do you have a TI-83 or similar calculator?

Do you have any Applied Math book? Lial and Hungerford is the text I would recommend for this.

PM me your phone number and I will help you do this over the phone. I ain't typing the answer.
 
UltF

UltF

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Math major in the house.

Demand equation you did it. Linear, obviously. The line of best fit is <meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="PowerPoint.Slide"><meta name="Generator" content="Microsoft PowerPoint 12">
y = -0.0142x + 6.5588​


so Revenue Function Your best price point was $3.50, where you made $780.50 on 223 loaves sold. So lets sell for $3.50 per loaf.
R(x)=3.50x, x<400

Cost function C(x) WEEKLY Interesting. Im not sure if you count 3500 as a one time cost. I wouldnt because you are paying for it monthly and shouldnt double count the oven. So I would say you are paying 177.97/(4 weeks) plus 1.182 per loaf.
C(x)=44.49 + 1.182x for the next 2 years. And then C(x)=1.182x . You can make from 0 to 400 loaves so your domain is 0 < x < 400. There is not enough info to factor in rent or electricity lol.

Profit function P(x) is your revenue - your cost. I assume we are ignoring taxes lol. So P(x)=R(x)-C(x)= 3.50x - 44.49 - 1.182x= 2.318x - 44.49

347 $1.50 $520.50 $65.86
330 $2.00 $660.00 $225.45
293 $2.50 $732.50 $341.68
245 $3.00 $735.00 $400.92
223 $3.50 $780.50 $472.42
177 $4.00 $708.00 $454.30

Max revenue see above.
column 3 is A * B = revenue
Max profit
Column 4 is column 3 minus C(x) = P(x)


Hopefully I don't have some huge flaw that makes all of that wrong lol.


I was also thinkign to make one long equation factorign in the two year loan where C(x) = 177.97 times 24 months divided by 104 weeks + cost per loaf
Then C(x) = 41.07 +1.182x
But I don't know if they want you to look at it that way. And you aren't paying extra for the loan forever so that doesn't work. I would just mention that the oven cost disappears after 2 years, increasing profit to 2.318x
 
RoofTop

RoofTop

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Messages
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Demand equation you did it. Linear, obviously. The line of best fit is
y = -0.0142x + 6.5588​


so Revenue Function Your best price point was $3.50, where you made $780.50 on 223 loaves sold. So lets sell for $3.50 per loaf.
R(x)=3.50x, x<400

Cost function C(x) WEEKLY Interesting. Im not sure if you count 3500 as a one time cost. I wouldnt because you are paying for it monthly and shouldnt double count the oven. So I would say you are paying 177.97/(4 weeks) plus 1.182 per loaf.
C(x)=44.49 + 1.182x for the next 2 years. And then C(x)=1.182x . You can make from 0 to 400 loaves so your domain is 0 < x < 400. There is not enough info to factor in rent or electricity lol.

Profit function P(x) is your revenue - your cost. I assume we are ignoring taxes lol. So P(x)=R(x)-C(x)= 3.50x - 44.49 - 1.182x= 2.318x - 44.49

347 $1.50 $520.50 $65.86
330 $2.00 $660.00 $225.45
293 $2.50 $732.50 $341.68
245 $3.00 $735.00 $400.92
223 $3.50 $780.50 $472.42
177 $4.00 $708.00 $454.30

Max revenue see above.
column 3 is A * B = revenue
Max profit
Column 4 is column 3 minus C(x) = P(x)


Hopefully I don't have some huge flaw that makes all of that wrong lol.


I was also thinkign to make one long equation factorign in the two year loan where C(x) = 177.97 times 24 months divided by 104 weeks + cost per loaf
Then C(x) = 41.07 +1.182x
But I don't know if they want you to look at it that way. And you aren't paying extra for the loan forever so that doesn't work. I would just mention that the oven cost disappears after 2 years, increasing profit to 2.318x


Here's my answer
 
UltF

UltF

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Sep 19, 2009
Messages
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LOL. Punk never came back to see his answer. Sure glad I wasted my time for nothing. I guess it was due that day.
 
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