SOLUTION: Im so lost doing this homework and I need help with these last problems, anything will help thanks in advance. These are the questions that I need help with Profit Function.

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Question 947783: Im so lost doing this homework and I need help with these last problems, anything will help thanks in advance. These are the questions that I need help with
Profit Function. Find P(x), the weekly profit for producing and selling x loaves of bread. (Hint: profit = revenue – cost.)
This is what I got for my R(x)=-0.02x^2+6.65x and for the cost I got C(x)=43.6+1.18x

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?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Profit Function. Find P(x), the weekly profit for producing and selling x loaves of bread. (Hint: profit = revenue – cost.)
This is what I got for my R(x)=-0.02x^2+6.65x and for the cost I got C(x)=43.6+1.18x
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?
The equation R(x) = -.02x^2 + 6.65x is a quadratic equation with maximum occurring at the axis of symmetry which is x = -b/(2a), find this
x = %28-6.65%29%2F2%28-.02%29
x = %28-6.65%29%2F%28-.04%29
x = 166.25 loaves of bread for max revenue
:
What is the max revenue? replace x with 166.25
R(x) = -.02(166.25^2) + 6.65(166.25)
R(x) = -552.78 + 1105.56
R(x) = $552.78 is max rev
:
Price per loaf: 553/166 = $3.33 for max revenue
:
:
Maximum Profit. P(x) = R(x) - c(x)
P(x) = -.02x^2 + 6.65x - (43.6 + 1.18x)
P(x) = -.02x^2 + 6.65x - 43.6 - 1.18x
combine like terms
P(x) = -.02x^2 + 5.47x - 43.6
:
Find the number of loaves that should be produced and sold in order to maximize
the profit. What is the maximum profit?
find the axis of symmetry of this equation
x = %28-5.47%29%2F%282%2A-.02%29
x = 136.75 loaves for max profit
:
Replace x in the original profit equation to find actual profit
P(x) = -.02(136.75^2) + 5.47(136.75) - 43.6
P(x) = -374 + 748 - 43.6
P(x) = $330.42 is max profit
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Conclusion. How many loaves of bread will you produce each week and how much will you charge for each loaf? Revenue/loaves sold: 553/137 = $4.04
Why? That's the number of loaves for max profit
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Note; this is my take my this problem, I am not completely sure that I did this right, but perhaps it give some guidance. CK