You are the manager of a firm that provides fill gravel to construction sites. You purchase the material from three different suppliers (A, B, and C) for $160/ton, $140/ton and $170/ton, respectively. and have a contract to meet weekly demand for gravel at four different sites. The available supply, demand, and per-unit shipping costs for your operation are presented in the table below:
For example, Supplier B can provide you a maximum of 1,206 tons of gravel per week at $140/tonand for every ton of that material you ship to Site 3, you incur a cost of $27.00. You are contracted to supply a total of 720 tons each week to Site 3.
Supplier | Site 1 | Site 2 | Site 3 | Site 4 | Supply |
A | $32 | $19 | $42 | $38 | 730 |
B | $42 | $38 | $27 | $36 | 1206 |
C | $24 | $18 | $26 | $29 | 672 |
Demand | 460 | 575 | 720 | 670 |
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Formulate a linear program that will identify the optimal shipment strategy for your operation to keep your overall costs as low as possible.
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