A firm has the following production function for smoke detectors: q = 4KL, where K is the amount of capital employed and

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A firm has the following production function for smokedetectors: q = 4KL, where K is the amount of capital employed and Lis the amount of labor employed. The price of capital is r = $8 andthe price of labor is w = $2.
a. Does the firm’s production function exhibit constant,increasing, or decreasing returns to scale? Briefly explain
. b. Find and graph the expansion path.
c. Suppose that an order of 1600 units of smoke detectors hasbeen placed. How much labor and capital should the firm employ inorder to minimize the (long run) cost of production? How much willit cost to produce the 1600 units?
d. Find the long-run total cost curve (LRTC) as a function of q,and derive the long-run average cost curve (LRAC), and the marginalcost curve (LRMC) for this firm.
e. For the following statement, please answer "True" or "False"(and shortly explain): This firm is experiencing economies of scaleat every level of output.