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Find the profit-maximizing output q by using first- and

A monopolist has demand and cost curves given by:

Q = 1,000 - 0.25P

TC = 500 + 50Q + Q²

Show work for all parts:

a. Find the equation for the inverse demand curve (P as a function of Q).

b. Show the total revenue function.

c. Show the marginal revenue function.

d. Show the marginal cost function.

e. Find the profit-maximizing output (Q) by using first- and second-order conditions for the profit function.

f. Use the inverse demand curve to find the profit-maximizing price.

g. Calculate the maximum profit for the monopolist.

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Business Management: Find the profit-maximizing output q by using first- and

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Business Management: Find the profit-maximizing output q by using first- and

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