The owner of the Hughes Car Wash believes that the relationship between the number of cars washed and the amount of labor employed is
Q = 0.8 + 4.5 L - 0.3 L2

where Q = the number of cars washed per hour
L = the number of people employed per hour.

The firm receives $5 for each car washed. The hourly wage rate is $4.50. The hourly cost of capital is $15. The firm uses 6 units of capital per hour.
a. How many people should Hughes Car Wash employ to maximize profit?
Decision rule: MRPL = MCL
MRPL = (MR) (MPL)
MRPL = ($5) (4.5 - 0.6 L) = 22.50 - 3 L
MCL = $4.50
22.50 - 3 L = 4.50
3 L = 18
L = 6

b. How many cars will it wash when it maximizes profit?

Q = 0.8 + 4.5 (6) - 0.3 (36)
Q = 17

Note: the cost of capital and units of capital has no impact on the solution. K is not in the production function.