Question

Minimize c=10x1 2x2 subject to 4x1 x2≥17 3x1 x2≥4 x1, x2≥0 . Form the dual problem.

Answer 1

To form the dual problem, follow these steps: identify the primal problem's objective function and constraints, introduce dual variables for each constraint, write the dual problem by maximizing the sum of the products of the dual variables and constraint coefficients, and ensure the dual problem's objective function is minimized.

Step-by-step explanation:

To form the dual problem, we need to follow these steps:

1. Identify the primal problem's objective function and constraints.
2. For each constraint in the primal problem, introduce a dual variable.
3. Write the dual problem by maximizing the sum of the products of the dual variables and the corresponding constraint coefficients.
4. The dual problem will have the same number of variables as the primal problem has constraints.
5. The dual problem's objective function will be minimized.

In this case, the primal problem has an objective function c = 10x1 + 2x2, and the constraints are 4x1 x2 ≥ 17 and 3x1 x2 ≥ 4. So, the dual problem would be:

Maximize z = 17y1 + 4y2

subject to:

• 4y1 + 3y2 ≤ 10
• y1, y2 ≥ 0