A company is considering opening warehouses in four cities: New York, Los Angele

Question

A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and Atlanta. Each warehouse can ship 10,000 units per week. The weekly fixed costs of keeping each warehouse open are $40,000 for New York, $50,000 for Los Angeles, $30,000 for Chicago and $25,000 for Atlanta. Region 1 of the company requires 8000 units per week, region 2 requires 7000 units per week, and region 3 requires 4000 units per week. The costs (including production and shipping) of sending one unit from a warehouse to a region are attached in the file spreadsheet below. The company wants to meet the weekly demands at minimum cost, subject to the preceding information and the following restrictions:

If the New York warehouse is opened, then the Los Angeles warehouse must also be opened.

At most two warehouses can be opened.

Either the Atlanta or the Los Angeles warehouse must be opened. (Note that “either A or B” means, one of three possibilities – just A, just B or both A and B)

1 Opening warehouses 3 Unit production and shipping costs Region 1 Region 2 Region 3 Fixed cost $40,000 $50,000 $30,000 $25,000 6 From NY LA Chicago Atlanta $15 535 550 526 $18 $35 10 11 Warehouses to open (1 if open, 0 if not) 12 NY Chicago Atlanta 14 15 16 17 Amount produced and shipped Region 1 Region 2 Region 3 Total Logical Capacity 0

Explanation / Answer

Considering Warehouse capacity (10000)and Region demand(Total 8000+7000+4000=19000) and other conditions:2 Warehouse to be opened There are two options OPTION A:NY+LA OPTION B:Chicago+Atlanta EVALUATION of Option A To Region1 Region2 Region 3 Total Fixed Cost Capacity From NY 8000 1000 9000 $40,000 10000 LA 7000 3000 10000 $50,000 10000 TOTAL 8000 7000 4000 $90,000 Total Cost=8000*20+7000*15+1000*50+3000*26+90000= $        483,000 EVALUATION of Option B To Region1 Region2 Region 3 Total Fixed Cost Capacity From Chicago 6000 4000 $30,000 10000 Atlanta 8000 1000 $25,000 10000 TOTAL 8000 7000 4000 $55,000 Total Cost=8000*24+6000*35+1000*50+4000*18+55000= $        579,000 NY+LA (OptionA) is selected Cost of operating Warehouse $90,000 Cost of production and shipping $        393,000 (8000*20+7000*15+1000*50+3000*26) Total Cost $483,000 To Amount Produced and shipped Region1 Region2 Region 3 Total From NY 8000 0 1000 9000 LA 0 7000 3000 10000 Chicago 0 0 0 Atlanta 0 0 0 Total 8000 7000 4000 Cost of operating Warehouse $90,000 Cost of production and shipping $        393,000 Total Cost $483,000

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