# Thread: Linear Programming Problem

1. ## Linear Programming Problem

Consider the linear programming problem below:

Minimize g(x,y,z,w) = x - 2y + 3z - 4w
subject to x + 2y + 3z + 4w >= 5;
-y - 2w >= -1
x,y,z,w >= 0

a. Show that the objective function is bounded below on the constraint set.
c. Find all extreme point candidates by considering the six constraints as equations and solving the (6 4) systems of linear equations obtained from these constraints by taking them four at a time.
d. Solve the linear programming problem.

Any help would be greatly appreciated. If you could help me on c and d especially, I'd be much obliged. Too many variables to work with and it's in 4d so I can't graph it out. Thanks.

2. Originally Posted by bambamm
Consider the linear programming problem below:

Minimize g(x,y,z,w) = x - 2y + 3z - 4w
subject to x + 2y + 3z + 4w >= 5;
-y - 2w >= -1
x,y,z,w >= 0

a. Show that the objective function is bounded below on the constraint set.
c. Find all extreme point candidates by considering the six constraints as equations and solving the (6 4) systems of linear equations obtained from these constraints by taking them four at a time.
d. Solve the linear programming problem.

Any help would be greatly appreciated. If you could help me on c and d especially, I'd be much obliged. Too many variables to work with and it's in 4d so I can't graph it out. Thanks.
Put $\displaystyle u=y+2w$ and $\displaystyle v=x+3z$ and minimise $\displaystyle h(u,v)=v-2u$ subject to $\displaystyle 1\ge u \ge 0$, $\displaystyle v \ge 0$

CB