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9. Suppose that the demand equation for a monopolist is p = 100 – 0.01.x and the cost function is C(x) = 50x + 10, 000. (a) Find the marginal cost. (b) Find the value of x that maximizes the profit and determine the corresponding price and total profit for this level of production. (Answer: Produce 2500 units and sell them at $75 per unit. The profit will be $52,500).

9. Suppose that the demand equation for a monopolist is p = 100 – 0.01.x and the cost function is C(x) = 50x + 10, 000. (a) Find the marginal cost. (b) Find the value of x that maximizes the profit and determine the corresponding price and total profit for this level of production. (Answer: Produce 2500 units and sell them at $75 per unit. The profit will be $52,500).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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9. Suppose that the demand equation for a monopolist is p = 100 – 0.01x and the cost function is C(x) = 50x + 10, 000. (a) Find the marginal cost. (b) Find the value of x that maximizes the profit and determine the corresponding price and total profit for this level of production. (Answer: Produce 2500 units and sell them at $75 per unit. The profit will be $52,500). 10. The total cost, in dollars, of producing x units of a certain product is given by C (x) = 8x + 20+ 100 and the average cost is defined by A(x) = C(x)/x. (a) Find A'(x) and C' (x). (b) Find the minimum of A(x) and the value xo at which it occurs. (c) Compare A(xo) and C'(xo).
Transcribed Image Text:9. Suppose that the demand equation for a monopolist is p = 100 – 0.01x and the cost function is C(x) = 50x + 10, 000. (a) Find the marginal cost. (b) Find the value of x that maximizes the profit and determine the corresponding price and total profit for this level of production. (Answer: Produce 2500 units and sell them at $75 per unit. The profit will be $52,500). 10. The total cost, in dollars, of producing x units of a certain product is given by C (x) = 8x + 20+ 100 and the average cost is defined by A(x) = C(x)/x. (a) Find A'(x) and C' (x). (b) Find the minimum of A(x) and the value xo at which it occurs. (c) Compare A(xo) and C'(xo).
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