Case $-$ A Transportation Problem

Consider the following network representation of a transportation problem.

$6-1-1.$png

Question

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

$($Round your answers to the nearest integer$)$

Let

x$11=$ amount shipped from Jefferson City to Des Moines

x$12=$ amount shipped from Jefferson City to Kansas City

x$13=$ amount shipped from Jefferson City to St$.$ Louis

x$21=$ amount shipped from Omaha to Des Moines

x$22=$ amount shipped from Omaha to Kansas City

x$23=$ amount shipped from Omaha to St$.$ Louis

Min

x$11+$

$15$

x$12+$

$9$

x$13+$

$8$

x$21+$

$8$

x$22+$

x$23$

s$.$t$.$

From Jefferson City x$11+$ x$12+$ x$13<=$

From Omaha x$21+$ x$22+$ x$23<=$

To Des Moines x$11+$ x$21=$

To Kansas City x$12+$ x$22=$

To St$.$ Louis x$13+$ x$23=$

x$11,$ x$12,$ x$13,$ x$21,$ x$22,$ x$23>=0$

Flag question: Question $2$

Question $21\mathrm{.}5$ pts

Case $-$ A Transportation Problem

Consider the following network representation of a transportation problem.

$6-1-1.$png

Question

Solve the linear program to determine the optimal solution.

$($Round your answer to the nearest integer.$)$

Amount Cost

Jefferson City$$Des Moines

Jefferson City$$Kansas City

Jefferson City$$St$.$ Louis

Omaha$$Des Moines

Omaha$$Kansas City

Omaha$$St$.$ Louis

Total