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- Homework Statement
- Hi, trying to figure out this Linear programming problem:

A congressman of Canada is responsible for the allocation of $400000 for programs and projects in his district. 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 expected number of votes gained per dollar spent for the various programs are as follows.

job training - 0.02

parks - 0.1

sanitation - 0.06

mobile library - 0.07

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

None of the programs can receive more than 50% and less than 6% of the total allocation.

The amount allocated to sanitation can not exceed the total allocated to the parks and mobile library programs.

The amount allocated to job training must at least equal the amount spent on sanitation.

What is the maximal expected number of votes the congressman can gain by distributing the money among the programs?

So far I have figured out the following:

maximize 0.02x1 + 0.01x2 +0.06x3 + 0.07x4

subject to:

xi <= 200,000

xi >= 24,000

x3 <= x2 +x4

x1 >= x3

But my constraints are wrong as it is not working in solver, does anyone have any suggestions on the constraints?

- Relevant Equations
- So far I have figured out the following:

maximize 0.02x1 + 0.01x2 +0.06x3 + 0.07x4

subject to:

xi <= 200,000

xi >= 24,000

x3 <= x2 +x4

x1 >= x3

So far I have figured out the following:

maximize 0.02x1 + 0.01x2 +0.06x3 + 0.07x4

subject to:

xi <= 200,000

xi >= 24,000

x3 <= x2 +x4

x1 >= x3

But when I try to solve this in solver, I get an error which means my contraints must be wrong. Any suggestions on what constaints to put?

maximize 0.02x1 + 0.01x2 +0.06x3 + 0.07x4

subject to:

xi <= 200,000

xi >= 24,000

x3 <= x2 +x4

x1 >= x3

But when I try to solve this in solver, I get an error which means my contraints must be wrong. Any suggestions on what constaints to put?