\"Ci\" stands for cost of holding 1 unit of inventory for 1 period. \"Ch\" stand

Question

"Ci" stands for cost of holding 1 unit of inventory for 1 period.

"Ch" stands for cost of hiring one worker

"CF" stands for cost of Firing a worker

24. Mr. Meadows Cookie Company makes a variety of chocolate chip cookies in the plant in Albion, Michigan. Based on orders received and forecasts of buy- ing habits, it is estimated that the demand for the next four months is 850, 1,260, 510, and 980, expressed in thousands of cookies. During a 46-day period when there were 120 workers, the company produced 1.7 ion cook- ies. Assume that the number of workdays over the four months are respectively 26, 24, 20, and 16. There are currently 100 workers employed, and there is no starting inventory of cookies. a. What is the minimum constant workforce required to meet demand over the next four months? Evaluate the cost of the plan derived in part (a). required constraints. b. Assume that c,-10 cents per cookie per month, cu = $100, and CF-$200. c. Formulate as a lincar program. Be sure to define all variables and include the

Explanation / Answer

Thus minimum constant Worforce required is 138(137.03 rounded off)

The total cost comes out to be

$       36,559,800

$       36,559,800

k= 0.307971014 Number of units produced by 1 worker in 1 day Ci $                    0.01 Ch $                      100 Cf $                      200 Months Working Days Units/Worker Cummulative Units/Worker Forcasted Demand Cummulative Forecasted Demand Minimum Workers Monthly Production Cummulative Monthly Production Ending Inventory (in thousands) Monthly holding Cost Hiring Cost Firing Cost 1 26 8.01 8.01 850 850 106.15 1105 1105 255 $                11,050 700 2 24 7.39 15.40 1260 2110 137.03 1020 2125 15 $                10,200 $                  3,100 3 20 6.16 21.56 510 2620 121.53 850 2975 355 $                  8,500 $                  3,200 4 16 4.93 26.49 980 3600 135.92 680 3655 55 $                  6,800 $                  2,800 Total 680 $       36,550,000 $            6,600.00 $            3,200.00 Total Cost $       36,559,800

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