A congressman’s district has recently been allocated $48 million for projects. T
ID: 3183427 • Letter: A
Question
A congressman’s district has recently been allocated $48 million for projects. The congressman has decided to allocate the money to five ongoing projects. However, the congressman wants to allocate the money in a way that will gain him the most votes in the upcoming election. The details of the five projects and votes per dollar for each project are given below.
Project Votes/dollar
________________________
Parks 0.10
Education 0.08
Roads 0.07
Health Care 0.10
Family Welfare 0.09
In order to also satisfy some local influential citizens, he must meet the following guidelines.
- None of the projects can receive more than 25% of the total allocation.
- The amount allocated to parks cannot exceed the amount allocated to family welfare.
- The amount allocated to education must be equal to or more than the amount spent on roads.
- All of the money must be allocated.
Formulate a linear programming model for the above situation by determining
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Explanation / Answer
He has to maximize the votes/dollar from the projects.
Let a,b,c,d,e, be the amounts allocated to different projects.
We have to find the values of a,b,c,d,e
Objective function : maximize 0.10 a + 0.08b+ 0.07c+0.10d+0.09e subject to
Constraints : a+b+c+d+e = 48
- All of the money must be allocated.
a<= 0.25(a+b+c+d+e)
b<= 0.25(a+b+c+d+e)
c<= 0.25(a+b+c+d+e)
d<= 0.25(a+b+c+d+e)
e<= 0.25(a+b+c+d+e)
- None of the projects can receive more than 25% of the total allocation.
- The amount allocated to education must be equal to or more than the amount spent on roads.
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