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# A grain cooperative with warehouses in Lincoln, Des Moines and Pierre must meet market demands in Denver, Kansas City, Minneapolis and St Louis. The following table summarizes data relevant to this w

A grain cooperative with warehouses in Lincoln, Des Moines and Pierre must meet market demands in Denver, Kansas City, Minneapolis and St Louis. The following table summarizes data relevant to this week’s distribution problem. The numbers in the first three rows and the first four columns are the transportation costs per unit from each warehouse to each market.

**From/To**

Denver

Kansas City

Minneapolis

St Louis

**Supply**

Lincoln

6

4

8

9

**750**

Des Moines

9

3

5

6

**750**

Pierre

9

11

6

14

**500**

**Demand**

**400**

**700**

**400**

**500**

(a) Construct a network representation of the problem of minimizing total transportation costs associated with shipping product from the warehouses to meet market demand.

(b) Formulate a LP model to solve this problem

(c) Suppose that the cooperative also has a warehouse in Omaha with a supply of 500 units and transportation costs to Denver, Kansas City, Minneapolis and St Louis of 6, 5, 7 and 9 respectively. Extend the LP formulation of (b) to include this option.

(d) Explain why the cost of meeting demand in part (c) cannot exceed the cost of meeting demand in (b).

(e) Solve the model given in part (c) using a spreadsheet optimization package, or by hand, as appropriate.