**Economics Output Maximization and Profit Maximization**

What you are solving for in these problems is the optimal input combination based either on what I call Solution #1 and Solution #2; Solution #1 guarantees output maximization and Solution #2 guarantees profit maximization. Use them where appropriate. Use the optimization procedure to get answers not an Excel result.

- The owner of the Hughes Car Wash believes that the relationship between the number of cars washed and the labor input is:

Q= -.8 + 4.5L – .3L2 where Q is the number of cars washed per hour and L is the number of people hours employed per hour.

The firm receives $5 for each car washed and the hourly wage rate for each person employed is $4.50. The cost of other inputs such as water is trivial and hence they are ignored.

- a) How many people should be employed to maximize profit?
- b) What will be the firm’s hourly profit?
- Find the optimal input combination for the following:

Q= 30X + 2XY -.5X2 -.5Y2 where Q is total output, X is worker hours, and Y is machine tool hours

Given that the price of X is $25.00 per unit of X and the price of Y is $40.00 per unit of Y and MR is $.50, find the optimal input combination for this production relationship.

- In the Elwyn Company, the relationship between output (Q) and the number of hours of skilled labor (S) and unskilled labor (U) is as follows:

Q= 300S + 200U -.2S2 -.3U2

The hourly wage of skilled labor is $10.00 per unit and the hourly wage of unskilled labor is $5.00 per unit. 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 decided 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 $10.00, how many hours of unskilled and how many hours of skilled labor should the company hire?

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