To build up the linear programming model that minimizes the total cost.
National Motors Corporation manufactures two different electrical motors for a single customer, Phoenix Appliance Company. Phoenix produces small kitchen appliances. One of National's motors (SMC500) is found in many of Phoenix's food processors, and another motor (SMC700) is used in assembly of Phoenix's blenders.
Three times each year, the procurement manager at Phoenix contacts National\'s marketing department to place a monthly order for each of the coming four months. Phoenix's demand for motors varies each month based on its own sales forecasts, production capacity, and financial position. National has just received the January-April order and must begin its own four-month production plan. Phoenix's order for SMC500 motors is 800 for January, 700 for February, 1,000 for March, and 1,100 for April. For the SMC700, Phoenix requires 1,000 in January, 1,200 in February, and 1,400 each in March and April.
National currently pays its workers $16.00 per hour, even though a labor agreement that goes into effect on March 1 will raise this figure by ten percent. The labor time required is 78 minutes for the SMC500 and 54 minutes for the SMC700. The company workforce provides 2,240 labor hours per month and the union contract has a "no-layoff" clause. This has led National to adopt a policy of always scheduling at least 2,240 hours of production each month. The contract allows national to add one or two skilled former employees (now retired) on an hourly basis at the going rate and use them up to 160 hours each per month to temporarily increase capacity.
Each SMC500 that is in inventory at the end of the month is estimated to cost the company 20 cents in holding cost for that month and each SMC700 costs the company 15 cents. This inventory, which is, in fact, the inventory on hand at the end of the previous month plus the current month's production less the amount shipped to Phoenix, is held in a storage area whose capacity is 3,300 motors of either type (the SMC500 and SMC 700 are similar in size). Because of the design modification in the motors, the January production will be the first of the new motors to be made. To organize for this, National has scheduled production for the end of the previous year in such a manner that the storage area will be empty on January first. National has also decided to build a small buffer stock of motors. To accomplish this, 450 SMC500 motors and 300 SMC00 motors will be in inventory at the end of April.
a. build up a model that can be used to minimize the total cost.
b. supply a table showing the production schedule; give the total cost and explain your solution.