5. (20 points) Consider a monopolist facing inverse demand function () = 64 (7) where = 1 + 2 + 3 denotes the monopolist's production across three plants 1, 2

and 3. The multiplant monopolist operates three plants, with marginal cost functions:

1(1) = 41 2(2) = 2 + 22 3(3) = 6 + 3

a) Derive multiplant marginal cost () function.

b) Using multiplant marginal cost () function derived in a), find the monopolist's

profit-maximizing price and output at each plant.

c) How would your answer to b) change if 2(2) = 4?

show work.