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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?


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.