Question

Unendo, is a large computer game manufacturer.

They have estimated that the demand function for their game "Star Wars Battlefront III" is as follows...

p = 76 - 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) = 16q + 5000;

where the fixed cost is $5000 and the marginal cost is $16 per game

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

Find ​the​ maximum​ profit they can earn.

(Round your answer to 2 decimal places, if necessary)

Answer 1

Find the revenue as

R=p*q = (76-0.05q)*q= 76q-0.05q²

Given cost as

C=16q+5000

Find profit as

P=R-C

P=(76q -0.05q²)-(16q+5000)

P=-0.05 q^2 + 60 q - 5000

Now to maximize, find derivative and then set to 0

P'= -0.1 q +60

set to 0

-0.1q +60 =0

0.1q =60

q=600

Substitute q = 600 to obtain

P=-0.05 *600 ^2 + 60 *600 - 5000

P=13,000

Hence,

profit is $13,000

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