2. (* * *) Dr. Bob sets up a new company, Alpha Electronics, producing specialized but low tech computer chips. The demand q in thousands of chips per month is related to the price p in dollars by q(p) = 20e P. Note that there is still demand q > 0 even for very large prices p (some consumers need these chips no matter the cost). The chip factory has fixed costs of $1,000 per month and each chip costs $1 to manufacture. (a) (1 mark) Find the inverse of the demand curve, the function p(q). (b) (2 marks) Find the profit function P(r) in thousands of dollars per month where r is the production of the factory in thousands per month matching demand (q = x). (c) (2 marks) Find the maximum profit per month and the corresponding production r. Give a short justification of how you know this is the maximum