Chapter 23, Problem 5PSA

1.

To determine

The contribution margin per machine hour for each product.

Answer to Problem 5PSA

Solution:

The contribution margin per machine hour for Product G and Product B is $200 and $70.

Explanation of Solution

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

Contribution margin per machine hour	Product G	Product B
Selling price per unit	$120	$160
Variable costs per unit	04	90
Contribution margin per unit	$80	$70
Machine hours to produce 1 unit	0.4	1
Contribution margin per machine hour	$200	$70

Table − 1

Conclusion

Hence, the contribution margin per machine hour for Product G and Product B is $200 and $70.

2.

To determine

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

Answer to Problem 5PSA

Solution:

The maximum unit of Product G is 440 units and the contribution margin is $35,200 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 G as possible. In single shift, the company can produce 176 hours per month.

Calculate the maximum output of G as shown below.

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

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

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

$\begin{array}{c}\text{Contribution}\text{margin}=440\text{units}\times \$80\text{per}\text{unit}\\ =\$\text{35,200}\end{array}$

Therefore, the contribution margin at recommended sales is $35,200.

Conclusion

The company should produce maximum units of Product G that is 440 units with contribution margin $35,200 per month.

3.

To determine

The units of Product G and Product B for another shift and the contribution margin for the mix.

Answer to Problem 5PSA

Solution:

The maximum possible unit of Product G and Product B is 880 and 112 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 G will be doubled once the second shift is added.

Calculate the maximum output of G as shown below.

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

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

The maximum level of Product G exceeds the company constraint for Product G that is 600 units per month. Therefore, the company should produce 600 units of Product G and allocate the remaining production capacity in the production of Product B.

Calculate the hours available for Product B as shown below.

Particulars	Amount
Units of Product G	600 units per month
Hours per unit	0.4
Hours used for Product G	240 hours
Hours available for Product B $\left(325\text{hours}-240\text{hours}\right)$	112 hours

Table − 2

Therefore, the hour available for Product B is 112 hours.

Calculate the maximum output of B as shown below.

$\begin{array}{c}\text{Maximum}\text{output}\text{of}B=\frac{112\text{hours}\text{per}\text{month}}{\text{1}\text{hour}\text{per}\text{unit}}\\ =112\text{units}\text{per}\text{month}\end{array}$

Therefore, the maximum output of B is 112 units per month.

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

Particulars	Units	Contribution/unit	Product B
Product G	600	80	$48,000
Product B	112	70	$7,840
Less extra shift costs			(15,000)
Total contributing margin			$40,840

Table − 3

Therefore, the contribution margin at recommended sales is $40,840.

Conclusion

It is clear from the above calculation that the contribution margin of $40,840 is quite higher than the margin of $35,200 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 5PSA

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 G to the extent, where it can sell 700 units by incurring additional marketing cost. This implies that 700 units of product G can be produced by the company and they can allocate its remaining productive capacity to product B.

Calculate the hours available for Product B as shown below.

Particulars	Amount
Units of Product G	700 units per month
Hours per unit	0.4
Hours used for Product G	280 hours
Hours available for Product B $\left(325\text{hours}-280\text{hours}\right)$	72 hours

Table − 4

Therefore, the hour available for Product B is 72 hours.

Calculate the maximum output of B as shown below.

$\begin{array}{c}\text{Maximum}\text{output}\text{of}B=\frac{72\text{hours}\text{per}\text{month}}{\text{1}\text{hour}\text{per}\text{unit}}\\ =722\text{units}\text{per}\text{month}\end{array}$

Therefore, the maximum output of B is 72 units per month.

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

Particulars	Units	Contribution/unit	Product B
Product G	700	80	$56,000
Product B	72	70	$5,040
Less extra shift costs			(15,000)
Less extra marketing costs			(12,000)
Total contributing margin			$34,040

Table − 5

Therefore, the contribution margin at recommended sales is $34,040.

Conclusion

It is clear from the above calculation that the contribution margin of $40,840 is quite lower than the margin of $40,840 obtained under the existing market constraints.