Question

Determine the dual problem. Solve either the original problem or its dual by the simplex method, and then give the solutions to both. Minimize 2x+y+4z subject to the constraints below.

⎩ x+y+z≥12
⎨ 4x+y≥49
⎧ x≥0,y≥0
z≥0
Determine the dual problem.subject to the following constraints.
⎩ u+4v≤
⎨ u+v≤
⎧ u≤
u≥0,v≥0

Answer 1

The dual problem for the given linear programming problem can be determined by converting the given problem into its dual form, and the solutions for both the original problem and its dual can be obtained using the simplex method.

Step-by-step explanation:

The dual problem for the given linear programming problem can be determined by converting the given problem into its dual form. In the dual problem, the objective is to maximize, and the constraints are reversed.

The dual problem for the given linear programming problem is:

Maximize u + 4v

subject to the constraints:

• u + v ≥ 2
• u + 2v ≥ 3
• u ≥ 0, v ≥ 0

To solve either the original problem or its dual by the simplex method, we need to set up the initial tableau and perform the iterations until an optimal solution is reached. The optimal solutions for the original problem and its dual can then be obtained from the final tableau.