Linear Programming; Formulate and Discuss (Appendix)
Colonial Corporation manufactures two types of electric coffeemakers, Regular and Deluxe. The major difference between the two appliances is capacity. Both are considered top-quality units and sell for premium prices. Both coffeemakers pass through two manufacturing departments: Plating and Assembly. Colonial has two assembly operations, one automated and one manual. The Automated Assembly Department has been in operation for one year and was intended to replace the Labor Assembly Department. However, Colonial’s business has expanded rapidly in recent months.
and both assembly operations are still being used. Workers have been trained for both operations and can be used in either department. The only difference between the two departments is the proportion of machine time versus direct labor used. Data regarding the two coffeemakers are presented in the following schedule.
Sales Data | ||
| Regular Model | Deluxe Model |
Selling price per unit | $ 45.00 | $ 60,00 |
Variable selling cost per unit | 3.00 | 3.00 |
Annual allocated fixed overhead | 900,000 | 900,000 |
Unit Variable Manufacturing Costs | ||||
Plating Department | ||||
| Regular | Deluxe | Labor Assembly | Automated Assembly |
Raw material: |
|
|
|
|
Casing | $7.75 | $14.50 | — | — |
Heating element | 6.00 | 6.00 | — | — |
Other | 8.25 | 8.25 | — | — |
Direct labor: |
|
|
|
|
At $10 per hour | 2.00 | 2.00 | — | — |
At $12 per hour | — | — | $3.00 | $.60 |
Manufacturing overhead: |
|
|
|
|
Supplies | 1.25 | 1.25 | 1.50 | 1.50 |
Power | 1.20 | 1.20 | .75 | 1.80 |
Machine Hour Data | |||
| Plating | Labor Assembly | Automated Assembly |
Machine hours required per unit | .15 | .02 | .05 |
Machine hours available per month | 25,000 | 1,500 | 5,000 |
Annual machine hours available | 300,000 | 18,000 | 60,000 |
Colonial produced and sold 600.000 Deluxe coffeemakers and 900,000 Regular coffeemakers last year. Management estimates that total unit sales could increase by 20 percent or more if the units can be produced. Colonial already has contracts to produce and sell 35,000 units of each model each month. Colonial has a monthly maximum labor capacity of 30,000 direct-labor hours in the Plating Department and 40,000 direct-labor hours for the assembly operation (Automated Assembly and Labor Assembly, combined). Sales, production, and costs occur uniformly throughout the year.
Required:
1. Colonial Corporation's management believes that linear programming could be used to determine the optimum mix of Regular and Deluxe coffeemakers to produce and sell. Explain why linear programming is appropriate to use in this situation.
2. Management has decided to use linear programming to determine the optimal product mix. Formulate and label the following:
b. Objective function
a. Constraints
Be sure to define your variables.
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