4. A firm can employ capital (K) and labor () to produce output using the following production function: f (L. K ) = 4K + L . The price of capital is $8, and the price of labor is $4. a) What input combination should be the firm use to produce @ units of output? b) What is the firm's total cost of production as a function of the amount of output, Q? c) What is its marginal and average cost of production? d) Suppose the price of labor falls to $1. What input combination should the firm use now to produce O units of output? What is its total, marginal, and average cost of production? e) Suppose that in the short run, the firm's capital stock is fixed at 5 units (the input prices are the same as in part d)). Describe the firm's optimal input combination as a function of Q. Derive the firm's short-run total, variable, and fixed cost functions. g) Derive the firm's short-run marginal, average, average variable, and average fixed cost functions