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.
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.
Chapter4: Economic Evaluation In Health Care
Section: Chapter Questions
Problem 7QAP
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Question
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,
Step 2
c. Profit is maximized at the point where differentiation of profit with respect to x (dP/dx) is zero.
Therefore, the number of units that will maximize profit is 50 units.
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