The first constraint is
x + y + z 40.
To turn it into an equation, we must add a slack variable s to the left-hand side, getting
The next constraint is
2x + y - z 10,
and we must subtract the surplus variable t to the left-hand side, getting
The last constraint is
- y + z 10,
and we must subtract the surplus variable u to the left-hand side, getting
Finally, the objective is
We must subtract 2x + 3y + z from both sides to get the desired equation:
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