Watson Corporation manufactures two products,Simple and Complex.The following annual information was gathered: Total annual fixed costs are $18,000.Assume Watson Corporation can produce and sell any mix of Simple or Complex at full capacity.It takes one hour to make one unit of Complex.However,Simple takes 50% longer to manufacture when compared to Complex.Only 120,000 hours of plant capacity are available.How many units of Simple and Complex should Watson Corporation produce and sell in a year to maximize profits?
A)an equal number of Simple and Complex
B)80,000 units of Simple and 0 units of Complex
C)0 units of Simple and 120,000 units of Complex
D)either Simple or Complex; it does not matter

Question

Watson Corporation manufactures two products,Simple and Complex.The following annual information was gathered:  Total annual fixed costs are $18,000.Assume Watson Corporation can produce and sell any mix of Simple or Complex at full capacity.It takes one hour to make one unit of Complex.However,Simple takes 50% longer to manufacture when compared to Complex.Only 120,000 hours of plant capacity are available.How many units of Simple and Complex should Watson Corporation produce and sell in a year to maximize profits?
A)an equal number of Simple and Complex 
B)80,000 units of Simple and 0 units of Complex 
C)0 units of Simple and 120,000 units of Complex 
D)either Simple or Complex; it does not matter

Quizplus · Accepted Answer

To determine the optimal production mix, we need to calculate the contribution margin per unit for each product.

For Complex: 
Selling price = $60 
Variable cost = $30 
Contribution margin = Selling price - Variable cost = $60 - $30 = $30

For Simple: 
Selling price = $80 
Variable cost = $40 
Contribution margin = Selling price - Variable cost = $80 - $40 = $40

Since Simple has a higher contribution margin per unit, we should produce and sell as many units of Simple as possible without exceeding the plant capacity.

It takes one hour to make one unit of Complex, but Simple takes 50% longer to manufacture. This means that it takes 1.5 hours to make one unit of Simple. To determine the maximum number of units of Simple that can be produced, we will use the following equation:

1.5x + 1x = 120,000

Where x is the number of units of Complex produced.

Solving for x:

2.5x = 120,000

x = 48,000

This means that we can produce 48,000 units of Complex and 72,000 units of Simple, for a total of 120,000 units.

The total contribution margin for this production mix is:

(48,000 x $30) + (72,000 x $40) = $1,680,000

Therefore, the optimal production mix is:

C) 0 units of Simple and 120,000 units of Complex.

Watson Corporation Manufactures Two Products,Simple and Complex