Question

Your company has developed a new videoconference gaming platform that allows players to see and hear their friends while they play together remotely. The sales can be modeled by q(p)= 350000-2430p^2

where p is the price of the app in dollars and q is the number of user accounts sold, and the cost of production is

C(q)= 3q+4500

Do all your work neatly labeled on your own paper.  

a. Write the revenue function R(p)

b. Write the cost function C(p)

c. Write the profit function P(p)

d. Use the derivative to find the app price that will maximize profit. Round to the nearest cent. $

e. What is the maximum profit, rounded to the nearest cent? $

f. When the profit is maximized, what is the average cost per user account, rounded to the nearest cent? $

Answer 1

(a)

Revenue function is given by

That is

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(b)

That is

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(c)

That is

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(d)

At maximum profit,

Price can not be negative.

Therefore

Price for maximum profit is given by

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(e)

Price for maximum profit is given by

Maximum profit is given by

That is

Maximum profit = $967900

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(f)

Price for maximum profit is given by

Therefore

When profit is maximized, average cost per user account is given by

That is

Average cost = $73492.5

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