You work for a drug manufacturing company that holds a patent on Hair Grow, the world's most effective drug for restoring hair. Your job is to analyze the pricing and investment decisions facing the firm. Your marketing group estimates that Hair Grow has the following demand curve:

P = 101 - .00002Q

1. Your marginal cost for producing a Hair Grow pill is $1. What is the profit-maximizing price and quantity? What is your profit?
2. Suppose that your production facility can only produce 1,000,000 pills. What is your optimal price and quantity given the production constraint? What are your profits?
3. Suppose that you could increase the capacity of your plant to 3,000,000 pills within a two year period for a cost of $30,000,000. Should you undertake the investment (for simplicity, assume you can borrow the funds for the expansion at a 0 percent interest rate)?