Is the Optimal Solution to This Problem Unique, or Is $\mathrm { MAX } \quad 5 \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 2 }$

question 66

Essay

Is the optimal solution to this problem unique, or is there an alternate optimal solution? Explain your reasoning.
$\mathrm { MAX } \quad 5 \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 2 }$
Subject ta:
$\begin{array} { l } 3 X _ { 1 } + 5 X _ { \mathbf { 2} } \leq 15 \\10 X _ { 1 } + 4 X _ { \mathbf { 2 } } \leq 20 \\X _ { 1 } , X _ { 2 } \geq 0\end{array}$ $\text {Changing Calls}$
$\begin{array}{llrrrrr}&&\text { Final} &\text {Reduced }&\text {Objective }&\text {Allowable}&\text { Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \\\hline \$ \mathrm{~B} \$ 4 & \text { Number to make: } \mathrm{X} 1 &2& 0 & 5& 1E+30& 0 \\\$ \mathrm{C} \$ 4 & \text { Number to make: } \mathrm{X} 2 & 0 & 0 & 2 &0 & 1E+30\end{array}$

$\text {Constraints}$
$\begin{array}{llrrrrr}&&\text { Final } &\text {Shadow} &\text { Constraint } &\text {Allowable} &\text { Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Price } & \text { R.H. Side } & \text { Increase } & \text { Decrease } \\\hline \$ \mathrm{D} \$ 8 & \text { Used } & 6&0 & 15 & 1E+30 &9 \\\$ \mathrm{D} \$ 9 & \text { Used } & 20 & 0.5 & 20 & 30 & 20 \\\end{array}$

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Definitions:

Gross Profit

A financial measurement obtained by deducting the cost of goods sold from the overall sales revenue.

Written Evidence

Documented proof or records that support claims or events, often used in legal and financial contexts.

Freight-Out

The cost associated with transporting goods from a warehouse to the customer, typically classified as a selling expense.

Operating Expenses

The costs related to the day-to-day operations of a business, excluding the cost of goods sold.