# Maximizing Profit and Cost and Demand Functions

A company manufactures and sells x air-conditioners per month. The monthly cost and price-demand equations are

C(x) = 180x + 20,0(X)

p = 220 - 0.001x 0 =< x <=100,000

(A) How many air-conditioners should the company manufacture each month to maximize its monthly profit? What is the maximum monthly profit, and what should the company charge for each air-conditioner to realize the maximum monthly profit?

(B) Repeat part (A) if the government decides to tax the company at the rate of $18 per air-conditioner produced. How much revenue will the government receive from the tax on these air-conditioners?

(C) Repeat part (A) if the government raises the tax to $23 per airconditioner. Discuss the effect of this tax increase on the government's tax revenue.

(D) Repeat part (A) if the government sets the tax rate at St per air-conditioner. What value of t will maximize the government's tax revenue? What is the government's maximum tax revenue?

https://brainmass.com/math/calculus-and-analysis/maximizing-profit-cost-demand-functions-128365

#### Solution Summary

It shows how to maximize the profit for the air conditioner manufacturer given the cost and price-demand equations. The solution is detailed and was rated '5/5' by the student who posted the question.