The Primal Problem Is
Min
2x₁ + 5x₂ + 4x₃ $\ge$

question 18

Essay

The primal problem is
Min
2x₁ + 5x₂ + 4x₃
s.t.
x₁ + 3x₂ + 3x₃ $\ge$ 30
3x₁ + 7x₂ + 5x₃ $\ge$ 70
x₁, x₂, x₃ $\ge$ 0
The final tableau for its dual problem is $$\begin{array} { c c | c c c c c | c } & & \mathrm { u } _ { 1 } & \mathrm { u } _ { 2 } & \mathrm {~s} _ { 1 } & \mathrm {~s} _ { 2 } & \mathrm {~s} _ { 3 } & \\\text { Basis } & \mathrm { c } _ { \mathrm { B } } & 30 & 70 & 0 & 0 & 0 & \\\hline \mathrm { u } _ { 2 } & 70 & 0 & 1 & 3 / 4 & 0 & - 1 / 4 & 1 / 2 \\\mathrm {~s} _ { 2 } & 0 & 0 & 0 & - 3 / 2 & 1 & - 1 / 2 & 0 \\\mathrm { u } _ { 1 } & 30 & 1 & 0 & - 5 / 4 & 0 & 3 / 4 & 1 / 2 \\\hline & z _ { \mathrm { j } } & 30 & 70 & 15 & 0 & 5 & 50 \\& \mathrm { c } _ { \mathrm { j } } - \mathrm { z } _ { \mathrm { j } } & 0 & 0 & - 15 & 0 & - 5 &\end{array}$$ Give the complete solution to the primal problem.

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