Spring, Inc. manufactures two products. It currently has 1,000 hours of direct labor and 2,000 hours of machine time available per month. The table below lists the contribution margin, labor and machine time requirements, and demand for each product. How much of each product should Spring manufacture per month?
A) 1,000 units of A and 2,000 units of B
B) 1,000 units of A and 0 units of B
C) 0 units of A and 2,000 units of B B.
D) 1,000 units of A and 250 units of B

Question

Spring, Inc. manufactures two products. It currently has 1,000 hours of direct labor and 2,000 hours of machine time available per month. The table below lists the contribution margin, labor and machine time requirements, and demand for each product.  How much of each product should Spring manufacture per month?
A) 1,000 units of A and 2,000 units of B 
B) 1,000 units of A and 0 units of B 
C) 0 units of A and 2,000 units of B B. 
D) 1,000 units of A and 250 units of B

Quizplus · Accepted Answer

To determine the optimal production plan, we need to calculate the contribution margin per unit of each product and the labor and machine time required per unit of each product.

Product A:
Contribution Margin = $30 - $15 - $5 = $10
Labor Required = 2 hours
Machine Time Required = 1 hour

Product B:
Contribution Margin = $40 - $20 - $10 = $10
Labor Required = 1 hour
Machine Time Required = 2 hours

Since both products have the same contribution margin per unit, we can use the labor and machine time constraints to determine the optimal production plan.

Let x be the number of units of Product A and y be the number of units of Product B.

The labor constraint is: 
2x + y ≤ 1,000 
The machine time constraint is: 
x + 2y ≤ 2,000

To graph the feasible region, we plot the two constraint inequalities on a graph and shade the area where both constraints are satisfied.

graph

The feasible region is the shaded triangle with vertices at (0,0), (500,0), and (500,750).

To determine the optimal production plan, we need to calculate the total contribution margin for each point in the feasible region and choose the point with the highest total contribution margin.

The total contribution margin is: 
10x + 10y

We can use the corner points of the feasible region to evaluate the total contribution margin:

Corner point (0,0): Total contribution margin = 0 
Corner point (500,0): Total contribution margin = 5,000 
Corner point (500,750): Total contribution margin = 10,000

Therefore, Spring should produce 1,000 units of Product A and 250 units of Product B to maximize its total contribution margin while satisfying its labor and machine time constraints.