Economics

A pharmaceutical company owns the patent to produce a drug that cures Alzheimer’s disease. The following equations describe the monopolist’s demand, total revenue, marginal revenue, total cost and marginal cost:

Demand: P = 300 – 10Q
Total Revenue: TR = 300Q – 10Q^2
Marginal Revenue: MR = 300 – 20Q
Total Cost: TC = 30 + 60Q + 5Q^2
Marginal Cost: MC = 60 + 10Q
Where Q is the quantity of bottles sold (in millions) and P is the price in US dollars.
a. Find the price and quantity that maximize the company’s profit.
b. What is the pharmaceutical company’s profit?
c. Find the price and quantity that would maximize social welfare.