Question: A network diagram between five locations is shown. The left-hand side of the graph is labeled Supplies and lists Jefferson City and Omaha. The right-hand

A network diagram between five locations is shown. The left-hand side of the graph is labeled "Supplies" and lists Jefferson City and Omaha. The right-hand side of the graph is labeled "Demands" and lists Des Moines, Kansas City, and St. Louis. Lines are shown between various locations. The following list contains the numbers placed on the graph.

Jefferson City: 55
Omaha: 40
Des Moines: 25
Kansas City: 15
St. Louis: 55

Jefferson CityDes Moines: 15
Jefferson CityKansas City: 9
Jefferson CitySt. Louis: 8

OmahaDes Moines: 8
OmahaKansas City: 11
OmahaSt. Louis: 26

The supplies, demands, and transportation costs per unit are shown on the network.

(a)

Develop a linear programming model for this problem; be sure to define the variables in your model.

Let

x₁₁ = amount shipped from Jefferson City to Des Moines
x₁₂ = amount shipped from Jefferson City to Kansas City
x₁₃ = amount shipped from Jefferson City to St. Louis
x₂₁ = amount shipped from Omaha to Des Moines
x₂₂ = amount shipped from Omaha to Kansas City
x₂₃ = amount shipped from Omaha to St. Louis

Min

x₁₁

x₁₂

x₁₃

x₂₁

x₂₂

x₂₃

s.t.

x₁₁

x₁₂

x₁₃

x₂₁

x₂₂

x₂₃

x₁₁

x₂₁

x₁₂

x₂₂

x₁₃

x₂₃

x₁₁, x₁₂, x₁₃, x₂₁, x₂₂, x₂₃ 0

(b)

Solve the linear program to determine the optimal solution.

	Amount	Cost
Jefferson CityDes Moines
Jefferson CityKansas City
Jefferson CitySt. Louis
OmahaDes Moines
OmahaKansas City
OmahaSt. Louis
Total

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