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

question 20

Essay

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

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Definitions:

Restaurant Industry

A sector of the economy comprising establishments primarily engaged in preparing and serving meals, snacks, and beverages for immediate consumption.

Metropolitan Area

A region consisting of a densely populated urban core and its less-populated surrounding territories, sharing industry, infrastructure, and housing.

Monopolistically Competitive

A business environment defined by numerous companies offering products that are alike but not exactly the same, providing them with a certain level of influence over the market.

Pure Monopolist

A market scenario where a single firm is the sole provider of a product or service, without any close substitutes, giving the firm significant market power to influence prices.