For the Following Linear Programming Problem
Max Z
-2x₁ $\le$ 7
1x₁ + X₂ + X₃

Essay

For the following linear programming problem
Max Z
-2x₁ + x₂ - x₃
s.t.
2x₁ + x₂ $\le$ 7
1x₁ + x₂ + x₃ $\ge$ 4
the final tableau is $$\begin{array} { c c | c c c c c c | c } & & \mathrm { x } _ { 1 } & \mathrm { x } _ { 2 } & \mathrm { x } _ { 3 } & \mathrm {~s} _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm { a } _ { 2 } & \\\text { Basis } & \mathrm { C } _ { \mathrm { B } } & - 2 & 1 & - 1 & 0 & 0 & - \mathrm { M } & \\\hline \mathrm { s } _ { 2 } & 0 & 1 & 0 & - 1 & 1 & 1 & - 1 & 3 \\\mathrm { x } _ { 2 } & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 7 \\\hline & z _ { j } & 2 & 1 & 0 & 1 & 0 & 0 & 7 \\& \mathrm { C } _ { \mathrm { j } } - \mathrm { z } _ { \mathrm { j } } & - 4 & 0 & 1 & - 1 & 0 & - \mathrm { M } &\end{array}$$
a.Find the range of optimality for c₁, c₂ , c₃.c₄, c₅ , and c₆.
b.Find the range of feasibility for b₁, and b₂.