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Use Slack Variables to Rewrite This Problem So That All MAX:2X1+7X2\mathrm { MAX } : \quad 2 \mathbf { X } _ { 1 } + 7 \mathbf { X } _ { \mathbf { 2 } }

Question 72

Essay

Use slack variables to rewrite this problem so that all its constraints are equality constraints.
MAX:2X1+7X2\mathrm { MAX } : \quad 2 \mathbf { X } _ { 1 } + 7 \mathbf { X } _ { \mathbf { 2 } }
Subject to:
5X1+9X2909X1+8X2144X28X1X20\begin{array} { l } \mathbf { 5 } \mathbf { X } _ { 1 } + \mathbf { 9 } \mathbf { X } _ { \mathbf { 2 } } \leq 90 \\\mathbf { 9 } \mathbf { X } _ { 1 } + \mathbf { 8 } \mathbf { X } _ { \mathbf { 2 } } \leq 144 \\\mathbf { X } _ { \mathbf { 2 } } \leq \mathbf { 8 } \\\mathbf { X } _ { 1 } \mathbf { X } _ { \mathbf { 2 } } \geq 0\end{array}

Correct Answer:

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