Find the profit-maximizing price, output, profit, and deadweight loss for the following cases. Also solve for the price elasticity of demand at the profit-maximizing price and quantity. Assume that MC is constant in each case. Include a hand-drawn graph that illustrates the profit-maximizing price and quantity, and identifies the firm's profit and the deadweight loss generated.

a. P = 110 - 2Q; MC = $10

b. P = 1400 - 10Q; MC = $400

c. P = 50 - 5 Q; MC=$0

d. P = 1100 - 0.5Q; MC = $100