Chapter 14, Problem 57P

Ozark Industries manufactures and sells three products, which are manufactured in a factory with four departments. Both labor and machine time are applied to the products as they pass through each department. The machines and labor skills required in each department are so specialized that neither machines nor labor can be switched from one department to another.

Ozark Industries’ management is planning its production schedule for the next few months. The planning is complicated, because there are labor shortages in the community and some machines will be down several months for repairs.

Management has assembled the following information regarding available machine and labor time by department and the machine hours and direct-labor hours required per unit of product. These data should be valid for the next six months.

Inventory levels are satisfactory and need not be increased or decreased during the next six months. Unit price and cost data that will be valid for the next six months are as follows:

Required:

1. 1. Calculate the monthly requirement for machine hours and direct-labor hours for the production of products M07, T28, and B19 to determine whether the monthly sales demand for the three products can be met by the factory.
2. 2. What monthly production schedule should Ozark Industries select in order to maximize its dollar profits? Explain how you selected this production schedule, and present a schedule of the contribution to profit that would be generated by your production schedule.
3. 3. Identify the alternatives Ozark Industries might consider so it can supply its customers with all the product they demand.

To determine

Calculate the monthly requirement for machine hours and direct labor hours for the production of products M07 and B19 to ascertain whether the monthly sales demand for the three products are met by the factory.

Explanation of Solution

Manufacturing overheads: Manufacturing overheads refers to the indirect factory- related cost that has occurred while manufacturing a product. Some of the examples of manufacturing overheads are indirect labor, indirect materials, factory building and indirect factory supplies.

The monthly requirement for machine hours is calculated as follows:

	Department
Product	1	2	3	4
M07	500 $(500\times 1)$	500 $(500\times 1)$	1,000 $(500\times 2)$	1,000 $(500\times 2)$
T28	400 $\left(400\times 1\right)$	400 $\left(400\times 1\right)$	0	800 $\left(400\times 2\right)$
B19	2,000 $(1,000\times 2)$	2,000 $(1,000\times 2)$	1,000 $(1,000\times 1)$	1,000 $(1,000\times 1)$
Total required	2,900	2,900	2,000	2,800
Total available	3,000	3,100	2,700	3,300
Excess (deficiency)	100	200	700	500

Table (1)

Note: Monthly requirement for “machine hours” is computed by multiplying the monthly unit sale of each product with the “machine time” required for each department.

The monthly requirement for direct-labor requirements is calculated as follows:

	Department
Product	1	2	3	4
M07	1,000 $(500\times 2)$	1,500 $(500\times 3)$	1,500 $(500\times 3)$	500 $(500\times 1)$
T28	400 $\left(400\times 1\right)$	800 $\left(400\times 2\right)$	0	800 $\left(400\times 2\right)$
B19	2,000 $(1,000\times 2)$	2,000 $(1,000\times 2)$	2,000 $(1,000\times 2)$	1,000 $(1,000\times 1)$
Total required	3,400	4,300	3,500	2,300
Total available	3,700	4,500	2,750	2,600
Excess (deficiency)	300	200	(750)	300

Table (2)

Due to the labor shortage in Department 3, the monthly sales demand cannot be met for all three products

Note: Monthly requirement for direct labor is computed by multiplying the monthly unit sale of each product with the direct labor required for each department.

To determine

Identify the monthly production schedule that Industry O must select in order to maximize its dollar profits, explain the manner in which the production schedule is selected, and present a schedule of the contribution to profit that is generated by the production schedule.

Explanation of Solution

Contribution Margin: The process or theory which is used to judge the benefit given by each unit of the goods produced is called as contribution margin.

“The aim is to increase contribution margin. Fixed costs are irrelevant. Direct-labor hours (DLH) are the scarce resource in Department 3. Industry must initially produce the product that maximizes contribution margin per unit of the scarce resource (DLH). In this situation, two products, M07 and B19, need direct-labor hours in Department 3”.

Calculate the contribution margin:

	M07	T28	B19
Sales price  (a)	$196	$123	$167
Variable costs
Direct material	$7	$13	$17
Direct labor	$66	$38	$51
Variable overhead	$27	$20	$25
Variable selling	$3	$2	$4
Total variable costs  (b)	$103	$ 73	$ 97
Contribution margin  $\left(\text{a}-\text{b}\right)$	$ 93	$ 50	$ 70

Note: Direct labor is computed by adding the direct labor of Department 1, Department 2, Department 3, and Department 4.

Table (3)

Product	Contribution Margin (a)	Department 3 DLH (b)	Contribution Margin per DLH $\left(\frac{\text{a}}{\text{b}}\right)$
M07	$93	$3	$31
B19	$70	$2	$35

Table (4)

Prepare the resulting production schedule:

Product	Units	Resulting production schedule Comments
M07	250	Produce as much as the constraint permits $\left\{\text{750}\left[\text{Table (2)}\right]\text{÷3 DLH per unit}\right\}$ Decreased production depends on its lower contribution margin per direct-labor hour.
T28	400	Produce up to monthly sales demand; unaffected by Department 3.
B19	1,000	Produce as much as possible to increase contribution margin per DHL.

Table (5)

Prepare the schedule of contribution margin by product:

Schedule of contribution margin by product
Product	Contribution Margin per Unit (a)	Units Produced (b)	Contribution to Profit $\left(\text{a×b}\right)$
M07	$93	250	$23,250
T28	$50	400	$20,000
B19	$70	1,000	$70,000
Total contribution margin			$113,250

Table (6)

To determine

Identify the alternatives considered by Industry O for supplying all the products demanded by the customers.

Explanation of Solution

Industry O must consider the following aspects for supplying the additional quantities of MO7.

• Functioning on an overtime basis”.
• “Subcontracting the additional units”.
• “Obtaining labor from outside the community”.