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1. Defining Q to be the level of output produced and sold, assume that the firm's cost function is given by the following relationship:
TC = 100 + 2Q + 0.30Q2
Furthermore, assume that the demand for the output of the firm is a function of price P given by the following relationship:
Q = 24 - 0.5P
(a) Defining total profit as the difference between total revenue and total cost, express in terms of Q the total profit function of the firm.
(b) Determine the output level where total profits are maximized.
(c) Calculate total profits and selling price at the profit maximizing output level.
2. Suppose a firm assesses its profit function as:
p = -10 - 48Q + 15Q2 - Q3
Calculate the output level which maximizes profits.
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