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QUESTION 5 LA local firm 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 unit. 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: Predicted Predicted Demand Production Demand Production Month Days (in $10,000) | Month Days (in $10,000) January February 22 340 July August September 24 375 16 380 12 310 March 21 220 19 175 April May 19 100 October 22 145 23 490 November 20 120 June 20 625 December 16 165 Inventory holding costs are based on a 25% 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. Assuming that shortages are not allowed, determine the minimum constant workforce that the company will need over the next year. b. Evaluate the total cost of the constant workforce plan found in part (a). c. Formulate this problem as a linear program. d. Solve the problem. Round the variables in the resulting solution and determine the cost of the plan you obtain.

QUESTION 5 LA local firm 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 unit. 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: Predicted Predicted Demand Production Demand Production Month Days (in $10,000) | Month Days (in $10,000) January February 22 340 July August September 24 375 16 380 12 310 March 21 220 19 175 April May 19 100 October 22 145 23 490 November 20 120 June 20 625 December 16 165 Inventory holding costs are based on a 25% 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. Assuming that shortages are not allowed, determine the minimum constant workforce that the company will need over the next year. b. Evaluate the total cost of the constant workforce plan found in part (a). c. Formulate this problem as a linear program. d. Solve the problem. Round the variables in the resulting solution and determine the cost of the plan you obtain.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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C. QUESTION 5 A local firm 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 unit. 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: Predicted Predicted Demand (in $10,000) | Month Production Production Demand Month Days Days (in $10,000) January 22 340 July 24 375 February 16 380 August 12 310 March 21 220 September 19 175 April 19 100 October 22 145 May 23 490 November 20 120 June 20 625 December 16 165 Inventory holding costs are based on a 25% 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. Assuming that shortages are not allowed, determine the minimum constant workforce that the company will need over the next year. b. Evaluate the total cost of the constant workforce plan found in part (a). c. Formulate this problem as a linear program. d. Solve the problem. Round the variables in the resulting solution and determine the cost of the plan you obtain.
Transcribed Image Text:C. QUESTION 5 A local firm 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 unit. 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: Predicted Predicted Demand (in $10,000) | Month Production Production Demand Month Days Days (in $10,000) January 22 340 July 24 375 February 16 380 August 12 310 March 21 220 September 19 175 April 19 100 October 22 145 May 23 490 November 20 120 June 20 625 December 16 165 Inventory holding costs are based on a 25% 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. Assuming that shortages are not allowed, determine the minimum constant workforce that the company will need over the next year. b. Evaluate the total cost of the constant workforce plan found in part (a). c. Formulate this problem as a linear program. d. Solve the problem. Round the variables in the resulting solution and determine the cost of the plan you obtain.
Expert Solution
Step 1

Solution:

Prepare the table as shown below:

Month Number of Working days Demand Forecasting Units per worker Cumulative units per worker Cumulative net demand Minimum workers  Monthly production Cumulative production Inventory
January 22 340 0.528 0.528 328 622 410.256 410.256 82.256
February 16 380 0.384 0.912 708 777 298.368 708.624 0.624
March 21 220 0.504 1.416 928 656 391.608 1100.232 172.232
April 19 100 0.456 1.872 1028 550 354.312 1454.544 426.544
May 23 490 0.552 2.424 1518 627 428.904 1883.448 365.448
June 20 625 0.48 2.904 2143 738 372.96 2256.408 113.408
July 24 375 0.576 3.48 2518 724 447.552 2703.96 185.96
August 12 310 0.288 3.768 2828 751 223.776 2927.736 99.736
September 19 175 0.456 4.224 3003 711 354.312 3282.048 279.048
October 22 145 0.528 4.752 3148 663 410.256 3692.304 544.304
November 20 120 0.48 5.232 3268 625 372.96 4065.264 797.264
December 16 165 0.384 5.616 3443 614 298.368 4363.632 920.632
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