You were recently hired to become the manager of the Roller Division at a major conveyor-manufacturing firm. Roller manufacturing is relatively simple, requiring only labor and one machine that cuts and crimps rollers, according to the following production function:

Q = LK^0.5

Where K=1 represents capital equipment and L is labor. The firm has already spent $50 on the unit of capital it owns. Workers at the firm are paid a competitive wage of 10$/hour.

Now suppose that the firm suddenly decides to double the quantity of output but only has a day to complete the order. Therefore, in that time, the amount of capital is fixed but labor hours are not.

a)How many workers must it employ?

b)How much will it cost to produce 200 rollers?

c)Suppose the firm could also vary capital, how much labor and capital should it employ to produce 200 rollers?

d)How much will it cost to produce 200 rollers in the long run? How much money is the firm sacrificing by not having the ability to choose its level of capital optimally in g)?