3. (25 points) Suppose that a firm's production function is given by f(x1, x2) = 4x1 + x2. Let the price of input 1 be $12 and the price of input 2 be $2. If the firm wants to produce 30 units of output, what is the minimized cost of doing so? Illustrate the firm's optimal choice of inputs with a graph.

4. (15 points) Derive the cost function c(w1, w2, y) of a firm whose production function is given by f(x1, x2) = min{x1, 2x2}, where x1 and x2 denote the quantities of inputs, w1 and w2 denote the input prices, and y denotes the output goal.