Chapter 11, Problem 29E

1.

To determine

Calculate the gross profit for each product in total and per square yard.

Explanation of Solution

Calculate the gross profit for each product in total and per square yard:

	Product
Particulars	Commercial	Residential
Sales:
$\left(28,000\times \$16\right)$	$448,000
$\left(6,000\times \$25\right)$		$150,000
Less: Cost of goods sold
Variable cost:
$\left(28,000\times \$10\right)$	$280,000
$\left(6,000\times \$15\right)$		$90,000
Fixed costs:
$\left(28,000\times \$4.667\right)$	$130,676
$\left(6,000\times \$1.50\right)$		$9,000
Gross profit	$37,324	$51,000
Gross profit per square yard:
$\left(\frac{\$37,324}{ 28,000}\right)$	$1.33
$\left(\frac{\$51,000}{ 6,000}\right)$		$8.50

Table (1)

2.

To determine

Calculate the contribution margin for each product in total and per square yard.

Explanation of Solution

Calculate the contribution margin for each product in total and per square yard:

	Product
Particulars	Commercial	Residential
Sales:
$\left(28,000\times \$16\right)$	$448,000
$\left(6,000\times \$25\right)$		$150,000
Less: Variable cost:
$\left(28,000\times \$10\right)$	$280,000
$\left(6,000\times \$15\right)$		$90,000
Gross profit	$168,000	$60,000
Contribution margin per square yard:
$\left(\frac{\$168,000}{ 28,000}\right)$	$6.00
$\left(\frac{\$60,000}{ 6,000}\right)$		$10.00

Table (2)

3 a.

To determine

Calculate the following:

1. a. Compute the contribution margin per labor hour for each product.
2. b. Compute the optimum product mix, on a weekly basis and state the number of square yards of each product that should be produced each week.
3. c. Draw a graph for this problem, similar to the solution presented in Exhibit.

Explanation of Solution

1. a. Compute the contribution margin per labor hour for each product:

	Product
Particulars	Commercial	Residential
Contribution margin per square yard (A)	$6	$10
Labor hours per square yard (B)	0.12	0.18
Contribution margin per labor hour $\left(\frac{\text{A}}{\text{B}}\right)$	$50	$55.56

Table (3)

1. b. Compute the optimum product mix, on a weekly basis and state the number of square yards of each product that should be produced each week.

Product	Hours (a)	Square yards $\left(\frac{\text{a}}{\text{Hour per sq yd}}\right)$
Residential:
$\left(8,000\text{ Sq}\text{. yds}\times \text{0}\text{.18 hour per square yard}\right)$	1,440	8,000
Commercial: at 0.12 hour per square yard
$\left(\text{4,600}-1,440\text{ hours}\right)$	$3,160	$26,333

Table (4)

1. c. Draw a graph for this problem, similar to the solution presented in Exhibit.

Figure (1)

4.

To determine

State the conceptual lesson that is associated with requirements 1 to 3.

Explanation of Solution

• The major conceptual lesson is that neither of the profit measures described in requirement 1 or 2 is useful for ascertaining the short-term optimum product mix in the presence of resource constraints.
• Thus, for this purpose, it is essential to distribute available labor hours on the basis of the contribution margins expressed on a per-labor-hour basis.

5.

To determine

Indicate the primary role of the management accountant in terms of addressing the short-term product- (or service-) mix problem.

Explanation of Solution

The following are the major role of the management accountant in the given context:

• To work with engineers for calculating the labor-hour consumption of each product, and
• To develop accurate estimates of the contribution margins for each product and.

Together, these inputs permits to provide an optimum short-term product mix.