Question

how could we use constraint and dual price to show the objective function value is the optimal?( I have 3 binding constraints, and 1 non-binding constraint and its dual price is 0. ) Please clarify how to do it. Thanks.

Answer 1

Given the primal problem, first, construct the dual problem.

You have four primal constraints. Hence, there will be four dual variables (say, y1, y2, y3, y4).

For the three binding constraints (say c1, c2, c3), you will have non-zero i.e. basic dual solutions. So, your y1, y2, and y3 will have non-zero values. The values will be as follows:

y1 = dual price of constraint c1
y2 = dual price of constraint c2
y3 = dual price of constraint c3

The fourth constraint is non-binding, so, the dual variable y4 will be non-basic i.e. zero. So, y4=0

Having the values of y1, y2, y3, and y4 known, you can compute the value of the dual objective. You already have the primal objective value. If the values of the dual objective and primal objective match, we will say that this is the optimal solution.

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More clarity can be given if you post the actual problem.