6. A political mailing will have several pages on the economy, the military, and

Question

6. A political mailing will have several pages on the economy, the military, and the environment. The total number of these pages in the booklet should be less than 100. For the target group that will receive the booklet, market research suggests that there will be a positive impact proportional to 5 times the number of pages on the economy, a positive impact proportional to 2 times the number of pages on the military, and a negative impact proportional to -4 times the number of pages on the environment. The candidate, however, insists that the number of pages on the environment exceed the number on the military by at least 5 and that the number of pages on the economy also exceed the number on the military by at least 5. Find the number of pages that should be devoted to the economy, the military, and the environment. Please post work because this was incorrectly answered before. I believe the solution is (44,25,30) I just wanted to see the work

Explanation / Answer

x,y,z be the pages for Eco, mili and envir.

x+y+z <100

P=5x+2y-4z is the positive impact.

z>y+5 and x>y+5

Hence y+5+y+5+y<100

y < 30.3

Let y < 30

Then z > 35 and x >35

As z is having negative impact on environment, z should be minimum

Hence y =25, z = 25+5 = 30, x = 99-(25+30) = 44

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