with expalnation please!! Use the following information to answer the following

Question

with expalnation please!!

Use the following information to answer the following 8 questions. Consider a profit maximizing perfectly competitive market where: TC = .9Q^3 - 175Q^2 + 12,000Q and the price $5500(Relevant range of Q is from 1 to 200; round your answers to two decimals) What is the profit maximizing Q the firm will produce? What is ATC at the profit maximizing Q? At what level of production is ATC minimized? What is the profit or a loss for this firm if it is maximizing profits? There will be entry in this market. True False What is the TR of selling 85 units? What is the TC of making 98 units?

Explanation / Answer

profit = PQ-TC

at prfit maxm

P = MC

MC = 2.7Q^2 -350Q + 12000

5500 = 2.7Q^2 - 350Q + 12000

solving above eqn

Q = 107.165,

Q = 22.464

TC at 107.165 = (.9*107.165^3)-(175*107.165^2)+(12000*107.165) = 383868.08

PQ = 5500*107.165 = 589407.5

profit (at 107.65) = 589407.5-383868.08 = $205539.42

Profit (at 22.464) = 5500*22.464-((.9*22.464^3)-(175*22.464^2)+(12000*22.464)) = $-64907.95

profit (at 200) = 5500*200-((.9*200^3)-(175*200^2)+(12000*200))=-$1500000

A)

so max profit is at Q = 107.165, profit = 589407.5

B)

ATC (at Q = 107.165) = (.9*(107.165^2))-175*107.165+12000 = $3582.02

C) ATC is minimized at,

ATC = .9Q^2)-175Q+12000

differentiating,

1.8Q-175 =0

at Q = 175/1.8 = 97.22 ATC will be minimized

E) true

D)

TR = 5500*85 = 467500

E)

TC = (.9*98^3)-(175*98^2)+12000*98 = $342372.8

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