Suppose a certain city has a monopoly cable-television company. This company has total costs TC = 0.25Q² + 15Q + 10. (Hint: using calculus, this means MC = 0.5Q + 15 since MC is the derivative of TC with respect to output.)

The demand in the community is approximated by the equation Q_d = 150 - 2P.

a. Graphically depict the demand curve as well as the marginal cost (MC) curve.

b. If the cable company is free to choose its own price P_m and quantity Q_m, graphically depict the monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome.

c. Compute and state the exact monopolist equilibrium price P_m and quantity Q_m that you depicted graphically.

d. What will be the profit made by the monopolist in this case? Please explain how you calculated this profit.