Solve This Problem Graphically $\mathrm { MAX } : \quad \mathbf { 8 \mathbf { X } _ { 1 } } + 4 \mathbf { X } _ { \mathbf { 2 } }$

question 5

Essay

Solve this problem graphically. What is the optimal solution and what constraints are binding at the optimal solution?
$\mathrm { MAX } : \quad \mathbf { 8 \mathbf { X } _ { 1 } } + 4 \mathbf { X } _ { \mathbf { 2 } }$
Subject to:
$$\begin{array} { l } 5 \mathbf { X } _ { 1 } + 5 \mathbf { X } _ { 2 } \leq 20 \\6 \mathbf { X } _ { 1 } + 2 \mathbf { X } _ { 2 } \leq 18 \\\mathbf { X } _ { 1 } , \mathbf { X } _ { \mathbf { 2 } } \geq 0\end{array}$$

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Definitions:

Positive Association

A relationship between two variables where an increase in one variable is associated with an increase in the other variable.

Strong Association

A term indicating a high level of correlation between two variables, suggesting that changes in one are closely linked to changes in the other.

Nonlinear

Referring to a relationship or equation that does not form a straight line when graphed, often indicating a more complex relationship between variables.

Negative

In mathematics, a negative number is a real number that is less than zero.