A district has been allocated $8 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. They are 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. His staffs estimates of the number of people that will be happy per dollar spent for the various programs are as follows:

Program Number of people will be happy per dollar

Job training 0.02

Parks 0.05

Sanitation 0.06

Mobile library 0.04

At this point, the congressman is also obligated to observe the following guidelines:

• None of the programs can receive more than 44% of the total allocation.
• The amount allocated to parks cannot exceed the total allocated to both the sanitation project and the mobile library.
• 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.

a. Formulate a linear programming model for this problem.

b. Solve the model by using the computer.

c. Indicate the amount allocated to each program.