A manufacturer has the following production function (where L is the number of manufacturing workers per hour and K is in units of machines per hour and output Q is in units per hour):

Q = 6 L+36 K

(This is 6 times the square root of L plus 36 times the square root of K.)

(You can also write this asF(L,K)=Q=6 L+36 K.Note that it is possible for this firm to produce with no capital at all (fully handmade) or with no labor at all (fully automated).)

This implies that MPL=3 K and MPk=18 K

(This is 3 divided by the square root of L and 18 divided by the square root of K.)

The wage is w=15 per hour and the rental cost of capital is r=30 per hour. Assume that the manufacturer has no fixed costs and no other production costs besides labor and capital. The manufacturer's output can be sold for a price of P=5.

How many of the following statements are correct?

• The optimal value for L is L=1.
• The optimal value for K is K=9.
• Output at the optimal levels of labor and capital is Q=114.
• The firm's production cost per hour at the optimal levels of labor and capital is 285.
• The firm's profit per hour at the optimal levels of labor and capital is 285.

Group of answer choices

a. All five of the statements are correct.

b. Only two of the statements are correct.

c. None of the statements are correct.

d. Only four of the statements are correct.

e. Only one of the statements is correct.

f. Only three of the statement are correct.