A firm uses two inputs x1 and x2 to produce output y. The production function is given by f(x1, x2) = x1 + x2. The price of input 1 is 1 and the price of input 2 is 2. The price of output is 10.

(e) Solve the firm's cost minimization problem. Derive the firm's cost function c(y).

(f) Find the profit maximizing choice of inputs x 1 and x 2 and output y . Calculate the firm's profit from these choices