Chapter 23, Problem 5PSB

1.

To determine

The contribution margin per machine hour for each product.

Answer to Problem 5PSB

Solution:

The contribution margin per machine hour for Product R and Product T is $100 and $35.

Explanation of Solution

Calculate the contribution margin per machine hour for each product as shown below.

Contribution margin per machine hour	Product R	Product T
Selling price per unit	$60	$80
Variable costs per unit	20	45
Contribution margin per unit	$40	$35
Machine hours to produce 1 unit	0.4	1
Contribution margin per machine hour	$100	$35

Table − 1

Conclusion

Hence, the contribution margin per machine hour for Product R and Product T is $100 and $35.

2.

To determine

The units of Product R and Product T should the company produce to operate with only one shift and total contribution margin each month.

Answer to Problem 5PSB

Solution:

The maximum unit of Product R is 440 units and the contribution margin is $17,600 per month.

Explanation of Solution

Sales mix recommendation: To the extent allowed by production and market constraints, the company should produce as much of Product R as possible. In single shift, the company can produce 176 hours per month.

Calculate the maximum output of R as shown below.

$\begin{array}{c}\text{Maximum}\text{output}\text{of}R=\frac{\left(8\times 22\right)\text{hours}\text{per}\text{month}}{\text{0}\text{.4}\text{hours}\text{per}\text{unit}}\\ =440\text{units}\text{per}\text{month}\end{array}$

Therefore, the maximum output of R is 440 units per month.

Calculate the contribution margin at recommended sales mix as shown below.

$\begin{array}{c}\text{Contribution}\text{margin}=440\text{units}\times \$40\text{per}\text{unit}\\ =\$17\text{,600}\end{array}$

Therefore, the contribution margin at recommended sales is $17,600.

Conclusion

The company should produce maximum units of Product R that is 440 units with contribution margin $17,600 per month.

3.

To determine

The units of Product R and Product T for another shift and the contribution margin for the mix.

Answer to Problem 5PSB

Solution:

The maximum possible unit of Product R and Product T is 880 and 132 units per month. The contribution margin is $40,840 per month.

Explanation of Solution

The sales mix recommendation is that the maximum possible output of the Product R will be doubled once the second shift is added.

Calculate the maximum output of R as shown below.

$\begin{array}{c}\text{Maximum}\text{output}\text{of}\text{R}=\frac{352\text{hours}\text{per}\text{month}}{\text{0}\text{.4}\text{hours}\text{per}\text{unit}}\\ =880\text{units}\text{per}\text{month}\end{array}$

Therefore, the maximum output of R is 880 units per month.

The maximum level of Product R exceeds the company constraint for Product R that is 550 units per month. Therefore, the company should produce 550 units of Product R and allocate the remaining production capacity in the production of Product T.

Calculate the hours available for Product T as shown below.

Particulars	Amount
Units of Product R	550 units per month
Hours per unit	0.4
Hours used for Product R	220 hours
Hours available for Product T $\left(325\text{hours}-220\text{hours}\right)$	132 hours

Table − 2

Therefore, the hour available for Product T is 132 hours.

Calculate the maximum output of T as shown below.

$\begin{array}{c}\text{Maximum}\text{output}\text{of}\text{T}=\frac{132\text{hours}\text{per}\text{month}}{\text{1}\text{hour}\text{per}\text{unit}}\\ =132\text{units}\text{per}\text{month}\end{array}$

Therefore, the maximum output of T is 132 units per month.

Calculate the contribution margin at recommended sales mix as shown below.

Particulars	Units	Contribution/unit	Product T
Product R	550	40	$22,000
Product T	132	35	$4,620
Less extra shift costs			(3,250)
Total contributing margin			$23,370

Table − 3

Therefore, the contribution margin at recommended sales is $23,370.

Conclusion

It is clear from the above calculation that the contribution margin of $23,370 is quite higher than the margin of $17,600 obtained from one shift alone. Hence, the management should try to add the second shift.

4.

To determine

To ascertain:

Whether the company pursues the given strategy and double the shift.

Answer to Problem 5PSB

Solution:

The company can pursue the given strategy and double the shift.

Explanation of Solution

The company can loosen up the market constraint for the sales of Product R to the extent, where it can sell 675 units by incurring additional marketing cost. This implies that 675 units of Product R can be produced by the company and they can allocate its remaining productive capacity to Product T.

Calculate the hours available for Product T as shown below.

Particulars	Amount
Units of Product R	675 units per month
Hours per unit	0.4
Hours used for Product R	270 hours
Hours available for Product T $\left(325\text{hours}-270\text{hours}\right)$	82 hours

Table − 4

Therefore, the hour available for Product T is 82 hours.

Calculate the maximum output of T as shown below.

$\begin{array}{c}\text{Maximum}\text{output}\text{of}\text{T}=\frac{82\text{hours}\text{per}\text{month}}{\text{1}\text{hour}\text{per}\text{unit}}\\ =82\text{units}\text{per}\text{month}\end{array}$

Therefore, the maximum output of T is 82 units per month.

Calculate the contribution margin at recommended sales mix as shown below.

Particulars	Units	Contribution/unit	Product T
Product R	670	40	$27,000
Product T	82	35	$2,870
Less extra shift costs			(3,250)
Less extra marketing costs			(4,500)
Total contributing margin			$22,120

Table − 5

Therefore, the contribution margin at recommended sales is $22,120.

Conclusion

Hence, it is clear from the above calculation that the contribution margin of $22,120 is quite lower than the margin of $23,370 obtained under the existing market constraints.