Algebraic Problem II - Monopoly with Quadratic Cost Function (10points)

Suppose a monopoly's inverse market demand curve is P = 13 - Q and its cost function is C(Q) = 25 + Q + (1/2)*Q². [ Hints: marginal revenue is equal to 13 - 2Qand marginal cost is 1+Q ]

(i) What is the profit-maximizing quantity and price if there is no price discrimination?

(ii) What is the monopolist's profit? Should the monopoly operate or shutdown?

Please solve this problem accurately and manually (without using chatgbt as it often makes calculation errors and Problems)

Solve both parts to the problem accurately and timely