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# Network Representation and Linear Transformation

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The distribution system for a company consists of two plants, three warehouses, and three customers. Plant capacities and shipping costs per unit (in \$) from each plant to each warehouse are as follows on Exhibit A attached.

Customer demand and shipping costs per unit (in \$) from each warehouse to each customer are as follows in Exhibit B attached.

Due to technical reasons items can not be shipped from Warehouse-1 to Customer-2 temporarily. In addition, direct shipments can be made from Plant-1 to Customer-1 at a costs of \$4 per unit and from Plant-2 to Customer-3 at a costs of \$2 per unit. Draw a network representation and formulate a linear programming model for this problem.

See attached file for charts related to this problem.

https://brainmass.com/math/optimization/network-representation-linear-transformation-595303

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Exhibit A

See attachment for chart.

Exhibit B

Let P be plant, W be warehouse and C be customer. The diagram is shown blow:

Now let xij be the units from plant i to warehouse j and let yjk be units from warehouse j to customer k.
So we want to minimize 4x11+3x12+5x13+6x21+2x22+4x23+y11+5y13+7y21+3y22+3y23+4y31+2y32+2y33
Subject to: x11+x12+x13â‰¤650
x21+x22+x23â‰¤450
y11+y21+y31=310
y12+y22+y32=270
y13+y23+y33=420
x11+x21=y11+y12+y13
x12+x22=y21+y22+y23
x13+x23=y31+y32+y33
xijâ‰¥0 and yijâ‰¥0

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!