So I'm trying to solve a linear programming problem but there is just something I keep missing.

The primal problem:

x1 + 2x2 + 3x3 + 3x4 <= 15000

2x1 + 4x2 + x4 + 3x4 <= 20000

3x1 + 2x2 + 5x3 + 3x4 <= 20000

x1 >= 1000

x2 >= 1000

Maximize x1 + x2 + 2x3 + 2x4. I know the optimal value is 10500 as I've solved it.

But now I'm trying to create a dual problem.

y1 + 2y2 + 3y3 + y4 >= 1

2y1 + 4y2 + 2y3 + y5 >= 1

3y1 + y2 + 5y3 >= 2

3y1 + 3y2 + 3y3 >= 2

Minimize 15000y1 + 20000y2 + 20000y3 + 1000y4 + 1000y5.

And this cannot be right. So what's wrong with it? Solving it using the dual simplex method doesn't result in the same optimization value as the primal problem hence I'm doing something wrong when formulating the dual problem...