Excel's Solver Tool Has Been Used in the Spreadsheet Below $\ge$

question 25

Essay

Excel's Solver tool has been used in the spreadsheet below to solve a linear programming problem with a minimization objective function and all $\ge$ constraints. $\text { Input Section }$
$\begin{array}{l}\text { Objective Function Coefficients }\\\begin{array}{c|c}\hline X & Y \\\hline 5 & 4\end{array}\end{array}$

$\begin{array}{|c|c|c|c|}\hline \text { Constraints } & & & \text { Req'd. } \\\hline \# 1 & 4 & 3 & 60 \\\hline \# 2 & 2 & 5 & 50 \\\hline \# 3 & 9 & 8 & 144 \\\hline\end{array}$
$\text { Output Section }$
$\begin{array}{|l|c|c|c|}\hline \text { Variables } & 9.6 & 7.2 & \\\hline \text { Profit } & 48 & 28.8 & 76.8 \\\hline\end{array}$

$\begin{array}{|c|c|c|}\hline \text { Constraint } & \text { Usage } & \text { Slack } \\\hline \# 1 & 60 & 1.35 \mathrm{E}-11 \\\hline \# 2 & 55.2 & -5.2 \\\hline \# 3 & 144 & -2.62 \mathrm{E}-11 \\\hline\end{array}$
a. Give the original linear programming problem.
b. Give the complete optimal solution.

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Definitions:

Maximum Pay Rate

The top limit on the amount of compensation an employee can receive for their position within an organizational pay structure.

Equal Interval Approach

A method in which data or measurements are organized into categories that are equally spaced, often used in statistical analysis or data representation.

Pay Grade Sizes

The levels or categories within an organization's pay structure that determine the range of salaries for different groups of jobs, based on their evaluation.

Natural Breaks

Points in data or a process where there is a significant gap or change, often used to categorize or segment information.