Question: A local semiconductor firm, Superchip, is planning its workforce and production levels over the next year. The firm makes a variety of microprocessors and uses sales dollars as its aggregate production measure. Based on orders received and sales forecasts provided by the marketing department, the estimate of dollar sales for the next year by month is as follows:
Production Predicted Demand
Month Days (in $10,000)
January 22 340
February 16 380
March 21 220
April 19 100
May 23 490
June 20 625
July 24 375
August 12 310
September 19 175
October 22 145
Novenber 20 120
December 16 165
Inventory holding costs are based on a 25 percent annual interest charge. It is anticipated that there will be 675 workers on the payroll at the end of the current year and inventories will amount to $120,000. The firm would like to have at least $100,000 of inventory at the end of December next year. It is estimated that each worker accounts for an average of $60,000 of production per year (assume that one year consists of 250 working days). The cost of hiring a new worker is $200, and the cost of laying off a worker is $400.
a. Formulate this as a linear program.
b. Solve the problem. Round the variables in the resulting solution and determine the cost of the plan you obtain.