Question

Unendo, is a large computer game manufacturer.

They have estimated that the demand function for their game "Call of Duty:WWIII" is as follows ...

p = 89 - 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) = 25q + 5000;

where the fixed cost is $5000 and the marginal cost is $25 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)

Answer 1

Profit is maximum where marginal cost is equal to marginal revenue

Marginal cost = 25q

Marginal revenue=-0.05q

MC = MR

MC =25

MR =DERIVATIVE OF (89q-0.05q power of 2)

=89-2*0.05q

=89-0.1q

MR=MC

89-0.1q=25

-0.1q=25-89

-0.1q=-64

q=64/0.1

q=640

Calculation of price

P=89-640*0.05=57

P=57

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