Given the Following Linear Programming Problem
Max
10x₁ + 12x₂ $\ge$

Essay

Given the following linear programming problem
Max
10x₁ + 12x₂
s.t.
1x₁ + 2x₂ $\ge$ 40
5x₁ + 8x₂ $\le$ 160
1x₁ + 1x₂ $\le$ 40
x₁, x₂ $\ge$ 0
the final tableau is $$\begin{array} { c c | c c c c c | c } & & \mathrm { x } _ { 1 } & \mathrm { x } _ { 2 } & \mathrm {~s} _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } & \\\text { Basis } & \mathrm { c } _ { \mathrm { B } } & 10 & 12 & 0 & 0 & 0 & \\\hline \mathrm { x } _ { 2 } & 12 & 0 & 1 & - 2.5 & - .5 & 0 & 20 \\\mathrm { x } _ { 1 } & 10 & 1 & 0 & 4 & 1 & 0 & 0 \\\mathrm {~s} _ { 3 } & 0 & 0 & 0 & - 1.5 & - 5 & 1 & 20 \\\hline & \mathrm { z } _ { \mathrm { j } } & 10 & 12 & 10 & 4 & 0 & 240 \\& \mathrm { c } _ { \mathrm { j } } - \mathrm { z } _ { \mathrm { j } } & 0 & 0 & - 10 & - 4 & 0 &\end{array}$$
a.Find the range of optimality for c₁ and c₂.
b.Find the range of feasibility for b₁, b₂, and b₃.
c.Find the dual prices.