Suppose a firm faces the input prices of labor and capital of w = 4 and r = 1, respectively. The firm's production function is q = 4 K 0.5 L 0.5 ,...

1.     Suppose a firm faces the input prices of labor and capital of w = 4 and r = 1, respectively. The firm's production function is q = 4K0.5L0.5, such that MPL = 2K0.5L-0.5 and MPK = 2K-0.5L0.5 Answer the following questions: [5 pts. each]

a.    What is the least-cost input combination required to produce 40 units of output?

b.    Suppose the firm is stuck with 16 units of capital and still wants to produce 40 units of output. Find the amount of labor input and total cost.