Greenberg Motors, Inc., manufactures two different electrical motors for sale under contract to Drexel Corp., a...

 

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Greenberg Motors, Inc., manufactures two different electrical motors for sale under contract to Drexel Corp., a well-known producer of small kitchen appliances. Its model GM3A is found in many Drexel food processors, and its model GM3B is used in the assembly of blenders. Three times each year, the procurement officer at Drexel contracts Irwin Greenberg, the founder of Greenberg Motors, to place a monthly order for each of the coming four months. Drexel's demand for motors varies each month based on its own sales forecasts, production capacity, and financial position. Greenberg has just received the January-April order and must begin his own four-month production plan. The demand for motors is shown in Table 8.2. MODEL GM3A GM38 JANUARY 800 1,000 FEBRUARY MARCH 700 1,000 1,200 1,400 APRIL 1,100 1,400 Production planning at Greenberg Motors must consider several factors: 1. The company must meet the demand for each of the two products in each of the four months (see Table 8.2). Also, the company would like to have 450 units of the GM3A and 300 units of the GM3B in inventory at the end of April, as demand in May is expected to be somewhat higher than demand in the previous months. 2. There is a carrying, or holding, cost for any inventory left at the end of the month. So producing too many extra units of either product may not be desirable. The carrying cost assigned to the GM3A is $0.36 per unit per month, while the carrying cost for the GM3B is $0.26 per unit per month. 3. The company has been able to maintain a no-layoff policy, and it would like to continue with this. This is easier if the labor hours used do not fluctuate too much from month to month. Maintaining a production schedule that would require from 2,240 to 2,560 labor hours per month is desired. The GM3A requires 1.3 labor hours per unit, while the GM3B requires only 0.9 labor hours. 4. Warehouse limitations cannot be exceeded without great additional costs. There is room at the end of the month for only 3,300 units of the GM3A and GM38 combined. Although these factors sometimes conflict, Greenberg has found that linear programming is an effective tool in setting up a production schedule that will minimize total cost. Production costs are currently $20 per unit for the GM3A and $15 per unit for the GM3B. However, each of these is due to increase by 10% on March 1 as a new labor agreement goes into effect. Formulate an LP for this problem. Greenberg Motors, Inc., manufactures two different electrical motors for sale under contract to Drexel Corp., a well-known producer of small kitchen appliances. Its model GM3A is found in many Drexel food processors, and its model GM3B is used in the assembly of blenders. Three times each year, the procurement officer at Drexel contracts Irwin Greenberg, the founder of Greenberg Motors, to place a monthly order for each of the coming four months. Drexel's demand for motors varies each month based on its own sales forecasts, production capacity, and financial position. Greenberg has just received the January-April order and must begin his own four-month production plan. The demand for motors is shown in Table 8.2. MODEL GM3A GM38 JANUARY 800 1,000 FEBRUARY MARCH 700 1,000 1,200 1,400 APRIL 1,100 1,400 Production planning at Greenberg Motors must consider several factors: 1. The company must meet the demand for each of the two products in each of the four months (see Table 8.2). Also, the company would like to have 450 units of the GM3A and 300 units of the GM3B in inventory at the end of April, as demand in May is expected to be somewhat higher than demand in the previous months. 2. There is a carrying, or holding, cost for any inventory left at the end of the month. So producing too many extra units of either product may not be desirable. The carrying cost assigned to the GM3A is $0.36 per unit per month, while the carrying cost for the GM3B is $0.26 per unit per month. 3. The company has been able to maintain a no-layoff policy, and it would like to continue with this. This is easier if the labor hours used do not fluctuate too much from month to month. Maintaining a production schedule that would require from 2,240 to 2,560 labor hours per month is desired. The GM3A requires 1.3 labor hours per unit, while the GM3B requires only 0.9 labor hours. 4. Warehouse limitations cannot be exceeded without great additional costs. There is room at the end of the month for only 3,300 units of the GM3A and GM38 combined. Although these factors sometimes conflict, Greenberg has found that linear programming is an effective tool in setting up a production schedule that will minimize total cost. Production costs are currently $20 per unit for the GM3A and $15 per unit for the GM3B. However, each of these is due to increase by 10% on March 1 as a new labor agreement goes into effect. Formulate an LP for this problem.

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