For a certain product, suppose that total costs are given by c(x) = 1600 + 1500x and total revenues by R(x) = 1600x-x2   (b) Find the profit function, p(x).  c) Find the number of units that will maximize profit. (d) Find the maximum profit.

Microeconomics
13th Edition
ISBN:9781337617406
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter8: Production And Costs
Section8.4: Costs Of Production: Total, Average, Marginal
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For a certain product, suppose that total costs are given by c(x) = 1600 + 1500x and total revenues by R(x) = 1600x-x2

 

(b) Find the profit function, p(x). 

c) Find the number of units that will maximize profit.

(d) Find the maximum profit.

Expert Solution
Step 1

b. Profit (P) is calculated by the difference between total cost [c(x)] and total revenue [R(x)]. Therefore,

Economics homework question answer, step 1, image 1

Step 2

c. Profit is maximized at the point where differentiation of profit with respect to x (dP/dx) is zero.

Economics homework question answer, step 2, image 1

Therefore, the number of units that will maximize profit is 50 units.

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