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.