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.