Question

Suppose that you have a feasible solution to the primal that has objective value 2 and feasible solution to the dual that has objective value 4. a) Is there enough information to determine if the primal problem is a maximization or minimization problem? If yes, determine if the primal problem is a maximization or minimization problem and explain your answer. b) Can you determine if the primal is unbounded? Explain your answer. c) Can you determine if the dual is unbounded? Explain_your answer. d) Can you determine if at least one of the two solutions are optimal? Explain your answer. e) Can you determine if at least one of the two solutions are not optimal? Explain your answer.

Answer 1

a) Based on the information given, we can determine whether the primal problem is a maximization or minimization problem.

The objective value in the primal is 2.

The objective value in the dual is 4.

Since the dual has a higher objective value than the primal, it implies that the primal is a minimization problem. In linear programming, the objective values in the primal and dual are related in such a way that the optimal value of the dual is always greater than or equal to the optimal value of the primal in a minimization problem.

b) We cannot determine if the primal is unbounded with the given information. To determine if the primal is unbounded, you would need to know more about the problem, such as the constraints and the dual values.

c) We cannot determine if the dual is unbounded with the given information. Just like in part b, determining if the dual is unbounded would require additional information about the problem's constraints and primal values.

d) Based on the information provided, we cannot determine if at least one of the two solutions (primal or dual) is optimal. You would need more information, such as the constraints and the specific values of the primal and dual variables, to make this determination.

e) Similarly, based on the information given, we cannot determine if at least one of the two solutions is not optimal. Additional information about the constraints and variable values is needed to assess the optimality of the solutions.

Explanation: