# Maximizing a linear equation!

1. May 24, 2012

### abhishek2301

Hello,

I want to maximize a linear equation: 4*a + 8*b + 7*c + 5*d + 9*e with the following constraints:
0<=(4*a + 8*b + 7*c + 5*d + 9*e)<=1
0<=a<=100; 0<=b<=100; 0<=c<=100; 0<=d<=100; 0<=e<=100

Can I solve this problem using linear programming?
Is there are any other method to do it?

Thanks!

2. May 24, 2012

### Number Nine

There are an infinite number of solutions. An obvious one would be to take b = c = d = e = 0 and a = 0.25.

3. May 24, 2012

### DonAntonio

Well, there're lots of solutions to your problem, for example:

$\displaystyle{a=\frac{1}{4}\,,\,b=c=d=e=0}$

$\displaystyle{b=\frac{1}{8}\,,\,a=c=d=e=0}$

etc...

$\displaystyle{a=\frac{1}{8}\,,\,b=\frac{1}{16} \, ,\, c=d=e=0}$

etc....until one dies out of boredom.

DonAntonio