Defining Q to be the level of output produced and sold, assume that the firm's cost function is given by the relationship
TC = 20 + 5Q + Q²
Furthermore, assume that the demand for the output of the firm is a function of price P given by the relationship
Q = 25 - P
a. Defining total profit as the difference between total revenue and total cost, express in terms of Q the total profit function for the firm. (Note: Total revenue equals price per unit times the number of units sold.)
b. Determine the output level where total profits are maximized.
c. Calculate total profits and selling price at the profit-maximizing output level.
d. If fixed costs increase from $20 to $25 in the total cost relationship, determine the effect of such an increase on the profit-maximizing output level and total profits.