What is the profit maximizing output for the firm, Microeconomics

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What is the profit maximizing output for the firm

Problem

The Smith shoes factory produces quality dress shoes. The market for quality dress shoes is monopolistically competitive. The company receives a report from a consulting firm concluding that the demand for curve for its product is Q = 40,000 - 500Q and its total cost function is

C(Q) = 270.000 + 28Q - 0.005Q2 + 0.000001Q3 (MC = 28 - 0.01Q + 0.000003Q2)

A. What is the profit maximizing output for this firm?

B. What is the profit maximizing price of the output of this firm?

C. How much profit (loss) does the firm make?

D. Should the firm actually produce in the short run or shut down?

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