# An Introduction to Linear Programming and Game Theory by Paul R. Thie By Paul R. Thie

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Compare the profit associated with this production schedule with the profit of the (7,9) production schedule of part (d). (f) Conclusion: Problems requiring integral answers may require special techniques. 4 T H E TRANSPORTATION M O D E L Transportation problems were one of the first types of problems analyzed in the early history of linear programming. The general problem arises when goods available at several sources, such as warehouses or plants, must be shipped to various destinations, such as retail outlets or distribution centers.

Continuing this argument, show that the optimal shipping schedule has x\ \ = 275, x\2 = 0, x\3 = 75, X21 = 0, X22 = 325, X23 = 225. (b) Extend the above approach to determine a minimal-cost shipping schedule if the link from Mill 2 to Plant 2 is not used. 2. Is the rental truck used? Formulate mathematical models for the following problems. ) 2. (a) A canned goods supplier has two warehouses serving four outlets. The East Coast Warehouse has 600 cases on hand and the West Coast Warehouse has 1000 cases on hand.

5. THE DYNAMIC PLANNING MODEL 43 Third-week costs: 350(35 + Hi+ H2- F2+ H3 - F3) + 125F3 + 3M3 + 5U3 Fourth-week constraints: 35+Hl+H2-F2+H3-F3+H4-F4 = T4 + I4+P4 H4 F4 < Hi +H2-F2+H3-F3 25P4 = D4 2000 + M4>2D4 Dx +D2+D3 +D4 = 3700 (all units must be delivered by the end of the fourth week) Fourth-week costs: 350(35 + Hl+H2-F2+H3-F3+H4- F4) + 125^3 + 3M4 At the end of the fourth week, any worker hired for this project and still employed must be laid off. Let F\$ denote this number.