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 "Call of Duty: WWIII" is as follows:

p = 80 - 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) = 17q + 5000;

where the fixed cost is $5000 and the marginal cost is $17 per game Unendo wishes to maximize the weekly profit of producing and selling the game.

Find the price, p, per game that generates maximum profit. (Round your answer to 2 decimal places, if necessary)

Explanation / Answer

Profit is maximum where marginal cost is equal to marginal revenue

Here marginal cost = 17q

Marginal revenue=-0.05q

MC = MR

MC =17

MR =DERIVATIVE OF (80q-0.05qpower of 2)

=80-2*0.05q

=80-0.1q

MR=MC

80-0.1q=17

q=630

Calculation of price

P=80-630*0.05

=48.5

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