SOLUTION: I'm having trouble solving this word problem: The cost of producing a plastic toy is given by the function C(x)=2x+35, where as x is the number of hundreds of toys. The revenue

Question 517851: I'm having trouble solving this word problem:
The cost of producing a plastic toy is given by the function C(x)=2x+35, where as x is the number of hundreds of toys. The revenue from toy sales is given by R(x)=-x�+122x-400. Since profit = revenue - cost, find the profit function P(x). Use this function to find the number of toys sold to produce a maximum profit. What is the maximum profit?
Now I know that I need to use R(x)-C(x)=P(x) which ends up being -x�+120x-435=P(x) I think but I'm not sure how to do the rest
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The cost of producing a plastic toy is given by the function C(x)=2x+35, where as x is the number of hundreds of toys. The revenue from toy sales is given by R(x)=-x�+122x-400. Since profit = revenue - cost, find the profit function P(x). Use this function to find the number of toys sold to produce a maximum profit. What is the maximum profit?
============================
P(x) = R(x) - C(x)
P(x) = -x^2 + 122x - 400 - (2x + 35) = -x^2 + 120x - 435
The profit is a maximum where dP(x)/dx = 0
dP/dx = -2x + 120 = 0 -> x = 60
So the numbers of toys sold to maximum profit = 60
The max profit = -(60^2) + 120*60 - 435 = $3165
The graph of the profit function is below:

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