Question

FlexSteal, marketed as a miracle brush-on sealant and baldness cure, is manufactured at three plants that are struggling to keep up with the demand at the four regional centers. The cost to ship a truckload from each of the existing plants to the regional centers is shown in the table. Note that the capacity and the total demand are both measured in truckloads. ​ Philadelphia Atlanta Dallas Los Angeles Capacity Plant 1 89 75 93 115 400 Plant 2 120 88 103 93 400 Plant 3 95 82 112 98 400 Total Demand 350 350 350 350 ​ The supply chain manager has explored plant construction costs in two other cities as well as the cost to ship a truckload from each of the plants to the regional centers. The current plan is to build another plant with a capacity of 400 to allow room for sales growth. The construction cost for the new plants and cost to ship to each of the regional centers is shown here. ​ Philadelphia Atlanta Dallas Los Angeles Cost to Build Plant A 94 78 95 95 $23,500 Plant B 95 88 88 94 $26,000

What is the lowest cost solution for the existing set of plants and regional centers?

$108,650

$107,450

$109,750

$106,850

Answer 1

Total cost

$106,850

Excel formulation:

Solver inputs:

From \ To	PH	ATL	DAL	LA	Total sent	capacity
plant 1	0	300	100	0	400	400
plant 2	0	0	50	350	400	400
plant 3	350	50	0	0	400	400
total received	350	350	150	350
total demand	350	350	350	350
	Variable
costs	PH	ATL	DAL	LA
plant 1	$89	$75	$93	$115
plant 2	$120	$88	$103	$93
plant 3	$95	$82	$112	$98
Total cost	$106,850