A producer produces good y using inputs x1 and x2 according to the production function y = x1^(alpha)x2^(beta) where alpha + beta <1. The factor prices are w1 and w2 (for input 1 and 2). The producer can sell as much as he wants at unit price p.
1) Derive the cost function c (x, y)
2) What is the producer's optimal profit as a function of (w1,w2, p)?