The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2.

$\begin{array} { l l } \text { Max } & 2 x _ { 1 } + x _ { 2 } \\ \text { s.t. } & 4 x _ { 1 } + 1 x _ { 2 } \leq 400 \\ & 4 x _ { 1 } + 3 x _ { 2 } \leq 600 \\ & 1 x _ { 1 } + 2 x _ { 2 } \leq 300 \\ & x _ { 1 } , x _ { 2 } \geq 0 \end{array}$

a.
Over what range can the coefficient of x₁ vary before the current solution is no longer optimal?
b.
Over what range can the coefficient of x₂ vary before the current solution is no longer optimal?
c.Compute the dual prices for the three constraints.

Question

The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2.

\begin{array} { l l } \text { Max } & 2 x _ { 1 } + x _ { 2 } \\ \text { s.t. } & 4 x _ { 1 } + 1 x _ { 2 } \leq 400 \\ & 4 x _ { 1 } + 3 x _ { 2 } \leq 600 \\ & 1 x _ { 1 } + 2 x _ { 2 } \leq 300 \\ & x _ { 1 } , x _ { 2 } \geq 0 \end{array}

a.
Over what range can the coefficient of x₁ vary before the current solution is no longer optimal?
b.
Over what range can the coefficient of x₂ vary before the current solution is no longer optimal?
c.Compute the dual prices for the three constraints.

Quizplus · Accepted Answer

The Answer of The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2. $\begin{array} { l l } \text { Max } & 2 x _ { 1 } + x _ { 2 } \ \text { s.t. } & 4 x _ { 1 } + 1 x _ { 2 } \leq 400 \ & 4 x _ { 1 } + 3 x _ { 2 } \leq 600 \ & 1 x _ { 1 } + 2 x _ { 2 } \leq 300 \ & x _ { 1 } , x _ { 2 } \geq 0 \end{array}$ a. Over what range can the coefficient of x₁ vary before the current solution is no longer optimal? b. Over what range can the coefficient of x₂ vary before the current solution is no longer optimal? c.Compute the dual prices for the three constraints.

The Optimal Solution of the Linear Programming Problem Is at the Intersection