Consider a firm that produces a single output good Y with two input goods: labor (L) and capital (K). The firm has a technology described by the production function f : R 2 + R+ defined by f(l, k) = 2l + 5k, where l is the quantity of labor and k is the quantity of capital. Suppose that input prices are (w, r) >> 0, where w is the wage rate (price of a unit of labor) and r is the interest rate (price of a unit of capital), and p > 0 is the price of the output good Y . (a) Formulate the firm's profit maximization problem. (b) Under what conditions on the prices (w, r, p) is there a solution to the profit maximization problem? (c) Under what conditions on the prices (w, r, p) is there a solution to the profit maximization problem where the firm is willing to supply a strictly positive quantity of output? (d) Suppose p = 1 and the firm supplies 100 units of output. Under what conditions does the firm use only labor to produce the output, and how much labor does the firm demand in that case?