Excel's Solver Tool Has Been Used in the Spreadsheet Below $\text { Input Section }$

question 5

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  constraints. $\text { Input Section }$

$\text { Objective Function Coefficients }$
$\begin{array}{|c|c|c|c|c|}\hline && x & y & \\\hline && 5 & 4 & \\\hline &&&&\\\hline &\text { Constraints } & & & \text { Req'd } \\\hline &\# 1 & 4 & 3 & 60 \\\hline &\# 2 & 2 & 5 & 50 \\\hline &\# 3 & 9 & 8 & 144 \\\hline\end{array}$

$\text { Output Section }$
$\begin{array}{|c|c|c|c|c|}\hline &&&&\\\hline &\text { Variables } & 9.6 & 7.2 & \\\hline &\text { Profit } & 48 & 28.8 & 76.8 \\\hline &&&&\\\hline &\text { Constraint } & \text { Usage } & \text { Slack } \\\hline &\# 1 & 60 & 1.35 \mathrm{E}-11 \\\hline &\# 2 & 55.2 & -5.2 \\\hline &\# 3 & 144 & -2.62 \mathrm{E}-11 \\\hline &&&&\\\hline\end{array}$
a.Give the original linear programming problem.
b.Give the complete optimal solution.

---

Definitions:

Thoracic Vertebrae

The twelve vertebrae located in the mid-back section of the vertebral column, providing attachment for the ribs and making up part of the thoracic cage.

Cervical Vertebrae

The seven vertebrae located in the neck region of the spine, known individually as C1 through C7.

Transverse Foramina

Holes found in the transverse processes of cervical vertebrae through which the vertebral artery and vein and sympathetic nerves pass.

Cervical Vertebrae

The uppermost seven vertebrae in the vertebral column, located in the neck, designated C1 through C7.