In the Elwyn Company, the relationship between output ( Q) and the number of hours of skilled labor ( S) and unskilled labor ( U) is
Q = 300S + 200U- 0.2S^2 - 0.3U^2
The hourly wage of skilled labor is $10, and the hourly wage of unskilled labor is $5. The firm can hire as much labor as it wants at these wage rates.
a. Elwyn's chief engineer recommends that the firm hire 400 hours of skilled labor and 100 hours of unskilled labor. Evaluate this recommendation.
b. If the Elwyn Company decides to spend a total of $5,000 on skilled and unskilled labor, how many hours of each type of labor should it hire?
c. If the price of a unit of output is $10 (and does not vary with output level), how many hours of unskilled labor should the company hire?