A firm produces tires by two separate processes that require different quantities of capital (K), labor (L), and raw materials (M). Process 1 requires one unit of K, four units of L, and two units of M to produce a tire yielding a $4 profit. Process 2 requires one unit of K, two units of L, and four units of M to produce a tire yielding a $6 profit. The available supply of capital is 10; of labor, 32; and of raw materials, 32.

a. Formulate and solve (by graphing) the firm’s profit-maximization problem.

b. Find the shadow prices of raw materials and labor.