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Q As a result of a recently passed bill, a congressman’s district has been allocated $4 million for programs and projects. It is up to the congressman to decide how to distribute the money. The congressman has decided to allocate the money to four ongoing programs because of their importance to his district—a job training program, a parks project, a sanitation project, and a mobile library. However, the congressman wants to distribute the money in a manner that will please the most voters, or, in other words, gain him the most votes in the upcoming election. His staff’s estimates of the number of votes gained per dollar spent for the various programs are as follows:

Program Votes/Dollar

Job training 0.02

Parks 0.09

Sanitation 0.06

Mobile library 0.04

In order also to satisfy several local influential citizens who financed his election, he is obligated to observe the following guidelines:

  1. None of the programs can receive more than 30% of the total allocation.
  2. The amount allocated to parks cannot exceed the total allocated to both the sanitation project and the mobile library.
  3. The amount allocated to job training must at least equal the amount spent on the sanitation project.

Any money not spent in the district will be returned to the government; therefore, the congressman wants to spend it all. The congressman wants to know the amount to allocate to each program to maximize his votes.

Formulate a linear programming model for this problem.


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