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

question 30

Essay

Excel's Solver tool has been used in the spreadsheet below to solve a linear programming problem with a maximization objective function and all $\le$ constraints. Input Section
$\begin{array}{l}\text { Objective Function Coefficients }\\ X & Y \\ 4 & 6\end{array}$

$\begin{array}{|c|c|c|c|}\hline \text { Constraints } & & & \text { Avail. } \\\hline \# 1 & 3 & 5 & 60 \\\hline \# 2 & 3 & 2 & 48 \\\hline \# 3 & 1 & 1 & 20 \\\hline\end{array}$
$\text { Output Section }$
$\begin{array}{|l|c|c|c|}\hline \text { Variables } & 13.333333 & 4 & \\\hline \text { Profit } & 53.333333 & 24 & 77.333333 \\\hline\end{array}$

$\begin{array}{|c|c|c|}\hline \text { Constraint } & \text { Usage } & \text { Slack } \\\hline \# 1 & 60 & 1.789 \mathrm{E}-11 \\\hline \# 2 & 48 & -2.69 \mathrm{E}-11 \\\hline \# 3 & 17.333333 & 2.6666667 \\\hline\end{array}$
a.Give the original linear programming problem.
b.Give the complete optimal solution.

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Definitions:

Evaluate

The process of determining the value of a mathematical expression.

Calculator

A device or software used for performing arithmetic operations and calculations.

Perfect Square

A number that is the square of an integer, meaning it can be expressed as the multiplication of an integer by itself.

Perfect Cube

A number that can be expressed as the cube of an integer.