A primal maximization problem is given. Solve both the primal and dual problems with the simplex method.
Maximize subject to

Question

A primal maximization problem is given. Solve both the primal and dual problems with the simplex method. ​
Maximize  subject to
​  ​

Quizplus · Accepted Answer

For convenience, we can rewrite the primal problem as:
Maximize -TB1243_00 subject to
TB1243_11
Then we set up the simplex tableau:

We can see that the primal problem has an optimal solution of -5, achieved when x1 = 1 and x2 = 0.

To solve the dual problem, we set up the following tableau:

We can see that the dual problem has an optimal solution of -5 as well, achieved when y1 = 3 and y2 = 0.

Therefore, the optimal value of the primal problem is -5 and the optimal value of the dual problem is also -5, indicating that strong duality holds.

Among the given choices, only option D has the correct primal and dual optimal solutions of -5, so the answer is D.

A Primal Maximization Problem Is Given