Unendo, a large computer game manufacturer has estimated that the demand functio

Question

Unendo, a large computer game manufacturer has estimated that the demand function for their game "Destiny 3" is as follows:

p = 90 - 0.05q;

where p is the price of a game and q is the number of game produced and sold per week.

They estimate that their cost function in dollars is

C(q) = 22q + 5000;

where the fixed cost is $5000 and the marginal cost is $22 per game

Unendo wishes to maximize the weekly profit of producing and selling the game.

Find the number, q, of units that produces maximum profit. (Round your answer to the nearest whole number)

Explanation / Answer

P = 90 - 0.05q

TR = P*q = 90q - 0.05q2

MR = 90 - 0.1q

MC = 22

The profit maximization condition is:

MR = MC

90 - 0.1q = 22

0.1q = 68

q = 68 / 0.1

= 680

Thus, 680 units will produce maximum profit.

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