Concept explainers
Calen Company manufactures and sells three products in a factory of three departments. Both labor and machine time are applied to the products as they pass through each department. The nature of the machine processing and of the labor skills required in each department is such that neither machines nor labor can be switched from one department to another.
Calen’s management is attempting to plan its production schedule for the next several months. The planning is complicated by the fact that labor shortages exist in the community and some machines will be down several months for repairs.
Following is 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 at least the next six months.
Calen believes that the monthly demand for the next six months will be as follows:
Inventory levels will not be increased or decreased during the next six months. The unit cost and price data for each product are as follows:
Required:
- 1. Calculate the monthly requirement for machine hours and direct labor hours for producing Products 401, 402, and 403 to determine whether or not the factory can meet the monthly sales demand.
- 2. Determine the quantities of 401, 402, and 403 that should be produced monthly to maximize profits. Prepare a schedule that shows the contribution to profits of your product mix.
- 3. Assume that the machine hours available in Department 3 are 1,500 instead of 2,700. Calculate the optimal monthly product mix using the graphing approach to linear programming. Prepare a schedule that shows the contribution to profits from this optimal mix. (CMA adapted)
1.
Calculate the monthly machine hours and direct labor hours for product 401, 402 and 403 and indicate whether the factory can meet monthly sales demand or not.
Explanation of Solution
Contribution margin: Contribution margin is a measurement of performance where only revenue and variable costs are taken into consideration. Hence, this measurement is useful in the evaluation of the probable outcomes of decisions including pricing decisions and other marketing strategies that affect primarily revenue and variable costs.
Calculate the monthly machine hours and direct labor hours for product 401, 402 and 403 and indicate whether the factory can meet monthly sales demand or not as follows:
Direct labor hours:
Particulars | Department 1 | Department 2 | Department 3 | Total |
Product 401: | ||||
Labor hours per unit (A) | 2 | 3 | 3 | |
Unit sold (B) | 500 units | 500 units | 500 units | |
Labor hours for Product 401 | 1,000 | 1,500 | 1,500 | 4,000 hours |
Product 402: | ||||
Labor hours per unit (A) | 1 | 2 | 0 | |
Unit sold (B) | 400 units | 400 units | 400 units | |
Labor hours for Product 401 | 400 | 800 | 0 | 1,200 hours |
Product 403: | ||||
Labor hours per unit (A) | 2 | 2 | 2 | |
Unit sold (B) | 1,000 units | 1,000 units | 1,000 units | |
Labor hours for Product 401 | 2,000 | 2,000 | 2,000 | 6,000 hours |
Totals | 3,400 hours | 4,300 hours | 3,500 hours | 11,200 hours |
Table (1)
Machine hours:
Particulars | Department 1 | Department 2 | Department 3 | Total |
Product 401: | ||||
Machine hours per unit (A) | 1 | 1 | 2 | |
Unit sold (B) | 500 units | 500 units | 500 units | |
Machine hours for Product 401 | 500 | 500 | 1,000 | 2,000 hours |
Product 402: | ||||
Machine hours per unit (A) | 1 | 1 | 0 | |
Unit sold (B) | 400 units | 400 units | 400 units | |
Machine hours for Product 401 | 400 | 400 | 0 | 800 hours |
Product 403: | ||||
Machine hours per unit (A) | 2 | 2 | 1 | |
Unit sold (B) | 1,000 units | 1,000 units | 1,000 units | |
Machine hours for Product 401 | 2,000 | 2,000 | 1,000 | 5,000 hours |
Totals | 2,900 hours | 2,900 hours | 2,000 hours | 7,800 hours |
Table (2)
In this case, company can meet the demand in all departments expect Department 3, because available labor hours for department 3 (2,750 hours) is less than the monthly requirement of 3,500 hours.
2.
Prepare a schedule of contribution to profits for the given product mix.
Explanation of Solution
Prepare a schedule of contribution to profit for the given product mix as follows:
In this case, department 3 in product 401 has more labor hour than the actual available hours. Hence, after meeting the demand the additional labor hours of Department 3 is used to produce the product 1 as a subsidy of department 1. Thus, department 1 would produce only 250 units
Particulars | Optimal output (A) | Contribution margin per unit (B) |
Total contribution |
Product 401 | 250 units | $93 (1) | $23,250 |
Product 402 | 400 units | $50 (2) | $20,000 |
Product 403 | 1,000 units | $70 (3) | $70,000 |
Total contribution margin | $113,250 |
Table (3)
Working note (1):
Calculate the contribution margin per unit for product 401.
Working note (2):
Calculate the contribution margin per unit for product 402.
Working note (3):
Calculate the contribution margin per unit for product 403.
3.
Compute the optimal monthly product mix using the graphical approach to linear program and calculate the contribution profit for the optimal mix.
Explanation of Solution
Compute the optimal monthly product mix using the graphical approach to linear program and calculate the contribution profit for the optimal mix as follows:
Machine constraint:
Direct labor constraint:
Demand constraint for each product:
Note: X denotes number of product produced in Product 401, Y denotes number of product produced in Product 402, and Z denotes number of product produced in Product 403.
Corner point | X-value | Y-value | W-value | |
A | 0 | 0 | 400 | $20,000 |
B | 500 | 0 | 400 | $66,500 |
C | 500 | 500 | 400 | $101,500 |
D | 250 | 1,000 | 400 | $113,250 |
E | 0 | 1,000 | 400 | $90,000 |
Table (1)
Figure (1)
Hence, contribution margin under optimal output is $113,250.
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