The number of constraints to the dual of the following problem is: Max Z = 3x₁ + 2x₂+ 6x₃
S.t.4x₁ + 2x₂ + 3x₃ $\geq$ 100
2x₁ + x₂ - 2x₃ $\leq$ 200
4x₂ + x₃ $\geq$ 200

Question

The number of constraints to the dual of the following problem is: Max Z = 3x₁ + 2x₂+ 6x₃
S.t.4x₁ + 2x₂ + 3x₃

\geq

100
2x₁ + x₂ - 2x₃

\leq

200
4x₂ + x₃

\geq

200

Quizplus · Accepted Answer

The dual of this problem has one variable for each constraint in the primal problem, and one constraint for each variable in the primal problem. In this case, the primal problem has 3 constraints (the three inequalities given), and 3 variables (x₁, x₂, and x₃). Therefore, the dual problem will have 3 constraints (one for each variable in the primal problem), and 3 variables (one for each constraint in the primal problem). As a result, the number of constraints in the dual problem is 3.

The Number of Constraints to the Dual of the Following ≥\geq≥

The Number of Constraints to the Dual of the Following $\geq$