Assignment:
A company manufactures and sells x air-conditioners per month. The monthly cost and price-demand equations are
C(x) = 180x + 20,000
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?
Provide complete and step by step solution for the question and show calculations and use formulas.