The management of Claypole Corporation has provided the following data concerning its two products-H59 and C92: The constrained resource is a particular machine that is available for 10, 100 minutes each month.Each unit of product H59 requires 5 minutes on this machine.Each unit of product C92 requires 3 minutes on this machine. The company is considering launching a new product that would have a variable cost of $88.00 per unit.It would require 11 minutes of the constrained resource.The absolute minimum acceptable selling price for the new product should be:
A)$89.80
B)$107.80
C)$110.00
D)$88.00

Question

The management of Claypole Corporation has provided the following data concerning its two products-H59 and C92:  The constrained resource is a particular machine that is available for 10, 100 minutes each month.Each unit of product H59 requires 5 minutes on this machine.Each unit of product C92 requires 3 minutes on this machine. The company is considering launching a new product that would have a variable cost of $88.00 per unit.It would require 11 minutes of the constrained resource.The absolute minimum acceptable selling price for the new product should be:
A)$89.80 
B)$107.80 
C)$110.00 
D)$88.00

Quizplus · Accepted Answer

The company has a limited amount of time on the constrained machine each month, with a total of 100 minutes.

Each unit of product H59 requires 5 minutes of machine time, meaning that a maximum of 100/5 = 20 units of H59 can be produced per month.

Each unit of product C92 requires 3 minutes of machine time, meaning that a maximum of 100/3 = 33.33 (rounded down to 33) units of C92 can be produced per month.

The new product requires 11 minutes of machine time, which means that a maximum of 100/11 = 9.09 (rounded down to 9) units of the new product can be produced per month.

To determine the minimum acceptable selling price for the new product, we need to calculate the contribution margin per unit.

The variable cost of the new product is given as $88.00 per unit, so the contribution margin per unit is:

Contribution margin per unit = selling price - variable cost
We do not know the selling price, so we'll use "x" as a placeholder:

Contribution margin per unit = x - $88.00

To maximize profitability, we want to produce as many units of the new product as possible within the constraints of the constrained resource.

We can produce a maximum of 9 units of the new product per month, and we must take into account the reduced production of H59 and C92 that occurs when we allocate machine time to the new product.

If we produce 1 unit of the new product, we will have to produce 0.2 fewer units of H59 and 0.33 fewer units of C92.

Therefore, the contribution margin per unit of the new product must be high enough to make up for the lost contribution margin from the reduced production of H59 and C92.

Let's calculate the contribution margin per unit for H59 and C92:

H59: selling price - variable cost = $171.60 - $108.00 = $63.60 
C92: selling price - variable cost = $154.80 - $100.00 = $54.80

If we produce 1 unit of the new product, we lose the contribution margin from 0.2 units of H59 and 0.33 units of C92:

Lost contribution margin per unit of new product = 0.2($63.60) + 0.33($54.80) = $15.06

Now we can calculate the minimum acceptable selling price for the new product:

Minimum acceptable selling price = variable cost + lost contribution margin 
Minimum acceptable selling price = $88.00 + $15.06 = $103.06

So the answer is B) $107.80, which is the closest option.

The Management of Claypole Corporation Has Provided the Following Data