Chapter 8, Problem 33BEB

1.

To determine

Calculate the contribution margin per hour of masseuse time for each type of massage.

Answer to Problem 33BEB

The contribution margin per hour of masseuse time for full body and trouble spots are $132 and $180 respectively.

Explanation of Solution

Contribution Margin:

Contribution margin can be defined as the amount of difference the sales revenue and the variable expense. It means the amount of sales left over after covering the variable expenses.

The following table represents the contribution margin per hour of masseuse time for each type of massage:

	Full body ($)	Trouble Spots ($)
Contribution margin per unit	198	90
Required masseuse time per massage1	1.50	0.5
Contribution margin per hour of masseuse time2	132	180

Table (1)

Therefore, the contribution margin per hour of masseuse time for full body and trouble spot are $132 and $180 respectively.

Working Notes:

1. Calculation of required masseuse time per massage for the full body:

$\begin{array}{c}\text{Required masseuse time}=\frac{\text{Time required in full body massage}}{\text{Number of minutes in an hour}}\\ =\frac{90\text{ minutes}}{60\text{minutes}}\\ =1.5\text{ hours}\end{array}$

Hence, the required masseuse time per massage for the full body is 1.50 hours.

Calculation of required masseuse time per massage for trouble spots:

$\begin{array}{c}\text{Required masseuse time}=\frac{\text{Time required in trouble spot massage}}{\text{Number of minutes in an hour}}\\ =\frac{30\text{ minutes}}{60\text{ minutes}}\\ =0.50\text{ hour}\end{array}$

Hence, the required masseuse time per massage for trouble spots is 0.50 hour.

2. Calculation of contribution margin per hour of masseuse time for the full body:

$\begin{array}{c}\text{Contribution margin per hour of masseuse time}=\frac{\text{Contribution margin per unit}}{\text{Required masseuse time}}\\ =\frac{\$198}{1.50}\\ =\$132\end{array}$

Hence, the contribution margin per hour of masseuse time for the full body is $132.

Calculation of contribution margin per hour of masseuse time for trouble spot:

$\begin{array}{c}\text{Contribution margin per hour of masseuse time}=\frac{\text{Contribution margin per unit}}{\text{Required masseuse time}}\\ =\frac{\$90}{0.50}\\ =\$180\end{array}$

Hence, the contribution margin per hour of masseuse time for trouble spot is $180.

2.

To determine

Calculate the optimal mix of the massages.

Answer to Problem 33BEB

The optimal mix of full body and trouble spot is 1,333 units and 8,000 units respectively.

Explanation of Solution

Since the contribution margin per hour of masseuse time for trouble spot is $180 which is more than the contribution margin per hour of masseuse time for a full body that is $132. Therefore, the masseuse time must be devoted to the trouble spot first till 8,000 massages and then the full body. Use the following formula to calculate the units of the full body:

$\text{Units of full body}=\frac{{\text{Total masseuse time}}^{\text{3}}}{\text{Required masseuse time per massage for full body}}$

Substitute 2,000 hours for the total masseuse time and 1.50 hours for the required masseuse time per massage for the full body in the above formula.

$\begin{array}{c}\text{Units of trouble spots}=\frac{2,000\text{ hours}}{1.50\text{ hour}}\\ =1,333\text{ units}\end{array}$

Therefore, the optimal mix of trouble spots and full body is 8,000 units and 1,333 units respectively.

Working Note:

3. First, calculate the total masseuse time:

$\begin{array}{c}\text{Total masseuse time}=\text{Time spent}\times \text{Number of maseuses}\\ =1,500\text{ hours}\times 4\\ =6,000\text{ hours}\end{array}$

Hence, the total masseuse time is 6,000 hours.

Calculation of masseuse time for trouble spot:

$\begin{array}{c}\text{Masseuse time for trouble spot}=\left(\begin{array}{l}\text{Maximum units of trouble spot}\\ \times \text{Required masseuse time}\end{array}\right)\\ =\left(8,000\text{ units}\times 0.50\text{ hours}\right)\\ =4,000\text{ hours}\end{array}$

Hence, the masseuse time for trouble spot is 4,000 hours.

Calculation of masseuse time for the full body:

$\begin{array}{c}\text{Masseuse time for full body}=\left(\begin{array}{l}\text{Total masseuse time}\\ -\text{Masseuse time for trouble spot}\end{array}\right)\\ =6,000\text{ hours}-4,000\text{ hours}\\ =2,000\text{ hours}\end{array}$

Hence, the masseuse time for the full body is 2,000 hours.

3.

To determine

Calculate the contribution margin earned for the optimal mix.

Answer to Problem 33BEB

The contribution margin earned for the optimal mix is $983,934.

Explanation of Solution

Use the following formula to calculate the contribution margin earned for the optimal mix:

$\begin{array}{c}\text{Contribution margin for optimal mix}=\left(\begin{array}{l}\text{Number of units of full body}\\ \times \text{Contribution margin per unit}\end{array}\right)+\\ \left(\begin{array}{l}\text{Number of units of trouble spot}\\ \times \text{Contribution margin per unit}\end{array}\right)\end{array}$

Substitute 1,333 units for the number of units of full body, $198 for contribution margin per unit of full body, 8,000 units for the number of units of trouble spot and $90 for contribution margin per unit of a trouble spot in the above formula.

$\begin{array}{c}\text{Contribution margin for optimal mix}=\left(1,333\text{ units}\times \$198\right)\\ +\left(8,000\text{ units}\times \$90\right)\\ =\$263,934+\$720,000\\ =\$983,934\end{array}$

Therefore, the contribution margin earned for the optimal mix is $983,934.