Refer to the Contois Carpets problem, for which the network representation is shown in Figure. Suppose that Contois has a beginning inventory of 50 yards of carpet and requires an inventory of 100 yards at the end of quarter 4.
a. Develop a network representation of this modified problem.
b. Develop a linear programming model and solve for the optimal solution.
Figure
NETWORK REPRESENTATION OF THE CONTOIS CARPETSPROBLEM

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Production Nodes Production Cost per Square Yard Demand Nodes 600 Quarter I Production Quarter 400 Demand 0.25 6 Quarter 2 500 Demand 300 Quarter 2 Production Inventory Cost per Square Yard0.25 500 Qarter 3 Quarter 3 400 Demand Production 0.25 400 Quarter 4 Quarter 4 400 Demand Production Production Capacities Production (arcs) Demands