# Thread: Finding the optimal solution to a Linear Program

1. ## Finding the optimal solution to a Linear Program

Hi there,

It's the beginning of a new quarter and I can tell my basic linear algebra is failing me at this point. I just need help solving a multi-dimensional linear program. So far this is the LP.

Maximize: 6*x1 + 3*x2 + 8*x3 + 3*x4 + 9*x5 + 5*x6
Subject to:
x1 + x2 <= 480
x3 + x4 <= 400
x5 + x6 <= 230
x1 + x3 + x5 <= 420
x2 + x4 + x6 <= 250
x1, x2, ..., x6 >= 0

From there I have no idea where to go. I know how to solve a two-dimensional LP graphically but I just can't figure this one out.

2. Originally Posted by hjhart
Hi there,

It's the beginning of a new quarter and I can tell my basic linear algebra is failing me at this point. I just need help solving a multi-dimensional linear program. So far this is the LP.

Maximize: 6*x1 + 3*x2 + 8*x3 + 3*x4 + 9*x5 + 5*x6
Subject to:
x1 + x2 <= 480
x3 + x4 <= 400
x5 + x6 <= 230
x1 + x3 + x5 <= 420
x2 + x4 + x6 <= 250
x1, x2, ..., x6 >= 0

From there I have no idea where to go. I know how to solve a two-dimensional LP graphically but I just can't figure this one out.