Question

Forecasted Demand Unit Costs Holding Costs Time period Microwave Refrigerator Dishwasher Microwave Refrigerator Dishwasher Refrigerator Dishwasher Microwave Range Range Range Spring 4287 4080 5135 5482 149 126 129 142 16 20 14 13 Summer Fall Winter 3937 5262 4261 3775 135 142 127 129 14 15 19 18 4991 5885 135 3989 4364 132 137 121 10 14 16 19 5618 5061 5430 4929 138 127 141 12 17 124 14 18 Number of units that can be made by one worker per period: Refrigerator Dishwasher Time period Ranges Microwave 269 274 Spring 227 255 Summer 295 353 465 301 361 Fall 276 383 308 374 247 288 Winter 398 Time period Summer Fall Winter Spring Costs of hiring 400 430 450 428 Costs of lay off Costs per worker 750 719 713 741 566 583 552 613

Sears produces 4 types of appliances (i.e. refrigerator, dishwasher, ranges, and microwave). There are currently 1,000 workers employed who can be hired and laid off at any time. Initial inventory is 500 units for refrigerators, and 420 units for dishwashers, 380 units for ranges and 450 for microwaves. The number of units that can be made by one worker, forecasted demand, unit costs, and holding costs, as well as costs of firing and hiring and cost per worker are all given above.

1. Develop the cost function for Sears.
2. List all of the constraints to minimize the cost.

Answer 1

Solution gien that information, They are types of appliances workers N= 1000 Se Fingerators - 500 Onits dishwashers - 420 whils ranges. = 380 units & microwaves = 450 cnits. Total unit Cost = unit cost x number of unit mode by 1000 woster per ferod. statement of Total unit cost - Refrigerator , Dishwasher Pange microwalge trome Total chil- I period 0 1494227 X1000 = 33,823,5000 Summer 35x353 x1000 =47,655,00 Gli 1324 276X1000 Fall / 236, 4321000 to 1388 37481000 –51, 612,000 11264255X1600 129x 261X 1000 1424274 11000 1131,562,000 l = 33130,000 = 34,701,000 =38,95,000 142.829581000 127x45x1000|1298 30181000 187429,000 -41,890,000 = 59, 055,000 = 38,829,000 1137 x 38381000 11358 308X2000 121836 / X1000 1174,164,000 1-52,471,000 =41,580,000 -43,681,000 1277 398 X12000 1248 247 8600 141 x 288 X1000 1173,394,000 -50,5461000 | -30,628000 – 40,608,000 winter/138x7

6080 Statement of polal Holding cost Total Refögontor Dishwashel langs micruitole thinking Sporing 16X500 = 8000 90X420 - 8400 143380-5320 133450 97,370 5650 Gomor 14X500=7000 15x420-alb 6300 19x280 18x450 98620 7220 78100 fall 10XSOV- 5000148420-5880 16x300= 19840 3,510 18550 winter 148500 - 700 18X470 -7560 12x380 17x450 34560 - 4650 67 680 statement of Total cost of tining Tral cost of lay off and rical cost- of wooters per period. Time Persiod Spring Summer Fall Winter Cost 400 X 1000 430 X1000 4 28 X100 450X100 " =400000 430000 428000 450000 1750 x 1000 719x100 78x1000 71481000 750000 719000 713.000 716000 83 X10D 546 XICTO 2X1000 =583,600 506000 613000 d. 1,733,000 1,715000 1673,000 1,777,000 Cost ofs por 613X100 1. Wotel 566000 Total Cost of -20s, too fall 174,164000 winter 173,394000 o statement of optimize cost Time Pood. spring Summer Trial unit | 139,566.000 187,429,000 Trial Holding 127,570 / 28,620 wohning 1,133,000 - Mod Gust 132,322,570 189,172,620 25,510 26,680 1,715000 1,693,000 4777000 175882,510 175, 77,680.
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