Problem 1 -
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:
|
Month
|
Production Days
|
Predicted Demand (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.
Problem 2 -
For the data in problem 1, determine the cost of the plan that changes the workforce size each period to most closely match the demand.
Problem 3 -
Pizza Nut is a producer of frozen pizza products. The company makes a profit of 5 TL for each regular pizza it produces and 7.50 TL for each deluxe pizza produced. Each pizza includes a combination of dough mix and topping mix. Currently the firm has 600 kg of dough mix and 200 kg of topping mix. Each regular pizza uses ½ kg of dough mix and 125 gr of topping mix. Each deluxe pizza uses ½ kg of dough mix and 250 gr of topping mix. Based on the past demand Pizza Nut can sell at most 600 deluxe pizzas and regular pizza production must be at least as many as deluxe pizzas. Formulate the LP.