A local semiconductor firm, Superchip, is planning its workforce and productionlevels over the next year. The firm makes a variety of microprocessors and usessales dollars as its aggregate production measure. Based on orders received and sales forecasts provided by the marketing department, the estimate of dollarsales for the next year by month is as follows:Production Predicted DemandMonth Days (in $10,000)January 22 340February 16 380March 21 220April 19 100May 23 490June 20 625July 24 375August 12 310September 19 175October 22 145November 20 120December 16 165Inventory holding costs are based on a 25 percent annual interest charge. It is anticipatedthat there will be 675 workers on the payroll at the end of the current year and inventorieswill amount to $120,000. The firm would like to have at least $100,000 of inventory at theend 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). Thecost 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 determinethe cost of the plan you obtain.

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
November 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.