The Warwick Manufacturing Company produces shovels for industrial and home use. Sales of the shovels are seasonal, and Warwick’s customers refuse to stockpile them during slack periods. In other words, the customers want to minimize inventory, insist on shipments according to their schedules, and will not accept backorders.
Warwick employs manual, unskilled laborers who require only basic training. Producing 1,000 shovels costs $3,500 on regular time and $3,700 on overtime. These amounts include materials, which account for more than 85 percent of the cost. Overtime is limited to production of 15,000 shovels per quarter. In addition, subcontractors can be hired at $4,200 per thousand shovels, but Warwick’s labor contract restricts this type of production to 5.000 shovels per quarter.
The current level of inventory is 30,000 shovels, and management wants to end the year at that level holding 1,000 shovels in inventory costs $280 per quarter. The latest annual demand forecast is as follows:
Quarter Demand
1 .......... 70,000
2 .......... 150,000
3 .......... 320,000
4 .......... 100,000
Total 640,000
Build a linear programming model to determine the best regular- time capacity plan. Assume the following:
• The firm has 30 workers now, and management wants to have the same number in quarter 4.
• Each worker can produce 4,000 shovels per quarter.
• Hiring a worker costs $1,000, and laying off a worker costs $600.