1. Unconstrained optimization:

(a) Find the values for x1, x2, x3 which maximize the function f(x)=1+x12x-x-3x3.

(b) If a monopolistic firm has a linear inverse demand function of the form p = 100-q where p is price (in ) and q is the number of units of output sold, and the firm has a constant marginal cost of 10 per unit, what is the revenue-maximizing output and price? What is the profit-maximizing output and price?