pricing and output decisions, economics homework help

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the demand and cost function for a company are estimated to be as follows:

P = 100 – 8Q

TC = 50+80Q-10Q^2 +0.6Q^3

a. what price should the company charge if it wants to maximize its profit in the short run?

b. what price should it charge if it wants to maximize its revenue in the short run?

c.suppose the company lacks confidence in the accuracy of cost estimates expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation. What difference would it make on the recommended profit-maximizing and revenue-maximizing prices?

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