Wood Carving Corporation manufactures three products. Because of a recent lack of skilled wood carvers, the corporation has had a shortage of available labor hours. The following per unit data relates to the three products of the corporation: Assume that Wood Carving only has 1,800 labor hours available next month. Also assume that Wood Carving can only sell 800 units of each product in a given month. What is the maximum amount of contribution margin that Wood Carving can generate next month given this labor hour shortage?
A) $12,000
B) $19,000
C) $19,600
D) $19,800

Question

Wood Carving Corporation manufactures three products. Because of a recent lack of skilled wood carvers, the corporation has had a shortage of available labor hours. The following per unit data relates to the three products of the corporation:  Assume that Wood Carving only has 1,800 labor hours available next month. Also assume that Wood Carving can only sell 800 units of each product in a given month. What is the maximum amount of contribution margin that Wood Carving can generate next month given this labor hour shortage?
A) $12,000 
B) $19,000 
C) $19,600 
D) $19,800

Quizplus · Accepted Answer

To maximize contribution margin, Wood Carving Corporation should focus on producing the products that generate the highest contribution margin per labor hour. The contribution margin per labor hour for each product is as follows:

Product A: $15 / 0.2 labor hours = $75 per labor hour
Product B: $24 / 0.4 labor hours = $60 per labor hour
Product C: $8 / 0.1 labor hours = $80 per labor hour

Product C generates the highest contribution margin per labor hour, so Wood Carving should focus on producing as much of Product C as possible with the limited labor hours available.

Assuming that Wood Carving produces all 800 units of Product C, they will use 800 * 0.1 = 80 labor hours, leaving them with 1,720 labor hours to allocate between Products A and B.

To maximize contribution margin, Wood Carving should use the remaining labor hours to produce the products that generate the highest contribution margin per unit. The contribution margin per unit for each product is as follows:

Product A: $15 - $7 = $8
Product B: $24 - $11 = $13
Product C: $8 - $2 = $6

Product B generates the highest contribution margin per unit, so Wood Carving should focus on producing as much of Product B as possible with the remaining labor hours.

Assuming that Wood Carving produces all 800 units of Product B with the remaining 1,720 labor hours, they will use 800 * 0.4 = 320 labor hours, leaving them with 1,400 labor hours to allocate between Products A and B.

To maximize contribution margin, Wood Carving should use the remaining labor hours to produce as much of Product A as possible.

Assuming that Wood Carving produces all 800 units of Product A with the remaining 1,400 labor hours, they will use 800 * 0.2 = 160 labor hours, leaving them with 1,240 labor hours unused.

The contribution margin generated by this production mix is as follows:
Product A: 800 * $8 = $6,400
Product B: 800 * $13 = $10,400
Product C: 800 * $6 = $4,800
Total contribution margin = $6,400 + $10,400 + $4,800 = $21,600

However, since Wood Carving can only sell 800 units of each product in a given month, the maximum amount of contribution margin they can generate is limited to the amount generated by producing 800 units of each product.

Assuming that Wood Carving produces 800 units of each product with the limited labor hours available, the contribution margin generated will be:
Product A: 800 * $8 = $6,400
Product B: 800 * $13 = $10,400
Product C: 800 * $6 = $4,800
Total contribution margin = $6,400 + $10,400 + $4,800 = $21,600

Since this is the maximum contribution margin that Wood Carving can generate with the given constraints, the answer is C) $19,600.

Wood Carving Corporation Manufactures Three Products