22. Grissom Products installs standard and deluxe storage sheds. Selected data related to each product is as follows:

Standard Deluxe
Sales price per unit $2,000 $4,000
Direct materials per unit 350 600
Direct labor per unit 250 350
Variable overhead per unit 100 200
Direct labor hours per unit 4 6

Most of the installation process of the sheds is done using direct labor. There are a maximum of 24,000 direct labor hours available each year.

If there is unlimited demand for both products, how many of each type of shed should be installed in order to maximize profits?

We can not solve the problem for you. You must show your own work. However, to guide you as to how to solve it:
1. Calculate contribution per unit
2. Divide the contribution margin per unit with the labor hour per unit. This will show which product gives a better contribution per labor hour.
3. Use the product with the highest contribution per labor hour as your answer.

However, it must be noted that eliminating one product may affect the sale of the other. It is necessary to arrive at an appropriate sales mix to maximize profits.

Just as Rehmanvohra has said, you got to demonstrate what work you've done on the problem, and where you're hitting the wall.

Here's a little hint or two to help kick it off for you. You're dealing with a Linear Constrained Optimization problem. You only have one constraint; namely the inequality

4S\ +\ 6D\ \leq\ 24,000

where S is the number of Standard sheds installed, and D is the number of Deluxe units. The expression "4S + 6D" represents the total direct labor hours required for any given mix of S-D units, and by the terms of the problem, this amount cannot exceed 24,000.

Let us know how you've proceeded.