A linear programming computer package is needed.

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown.

$\backslash$table$[[$Constraint$,$Television,Radio,Online$],[$Audience per advertisement,$300,000,54,000,120,000],[$Cost per advertisement,$$2,000,$$$300,$$$600$

Consider the following network representation of a transportation problem.

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

$x_{11}=$ 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

s$.$t$.$

From Jefferson City

From Omaha

To Des Moines

To Kansas City

To St$.$ Louis

$x_{{11}^{\text{'}}}{x}_{{12}^{\text{'}}}{x}_{{13}^{\text{'}}},x_{{21}^{\text{'}}},x_{{22}^{\text{'}}}{x}_{23}0$

$($b$)$ Solve the linear program to determine the optimal solution.

$\backslash$table$[[,$Amount,Cost$],[$Jefferson City$-$Des Moines,,$],[$Jefferson City$-$Kansas City,,$],[$Jefferson City$-$St$.$ Louis,,$],[$Omaha$-$Des Moines,,$],[$Omaha$-$Kansas City,,$],[$Omaha$-$St$.$ Louis,,$],[,,],[$Total$,,]]$