The sate of Florida has recently been allocated $45 million for projects. The go

Question

The sate of Florida has recently been allocated $45 million for projects. The governor has decided to allocate the money to four ongoing projects. However, the governor wants to allocate the money in a way that will gain him the most votes in the upcoming election. The details of the four projects and votes per dollar for each project are given below.

Project              Votes/dollar

________________________

Parks                      0.07

Education               0.08

Roads                     0.09

Health Care            0.11

Family Welfare      0.08

In order to also satisfy some local influential citizens, he must meet the following guidelines.

- None of the projects can receive more than 30% of the total allocation.

- The amount allocated to education cannot exceed the amount allocated to health care.

- The amount allocated to roads must be equal to or more than the amount spent on parks.

- 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.

Note: Do NOT solve the problem after formulating.

Explanation / Answer

here .. OBJECTIVE FUNCTION : S1X+S2Y+S3Z+S4S+5=45

step 1 : [S1,S2,S3,S4,S5](0.07,0.08,0.09,0.11,0.09)=(8,11,8,10,8)

S1X+0.07=8

S2Y+0.08=11

S3Z+0.09=8

S4S+0.11=10

S5T+0.09=8

Here the desicion variables are 8,11,8,10,8

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