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i find it time consuming having to solve all the equations in a linear programming problem so as to find the optimal solution .how do i slide the iso contribution line in order to find the optimal solution?
Keeping it parallel you move it away from the original as far as you can without leaving the feasible region. The furthest corner of the feasible region is the optimal solution.
You certainly should not solve all the equations – the examiner expects you to use the iso-contribution line.
For more, you really should watch the free lecture on linear programming.
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