You Have Been Given the Following Linear Programming Model and Excel

question 18

Essay

You have been given the following linear programming model and Excel spreadsheet to solve this problem. What numbers should be entered into cells B5:C5 and B8:C10 to implement this model?
MIN: $\quad 8 X _ { 1 } + 3 X _ { 2 }$
Subject to: $\quad X _ { 2 } \geq 8$
$\begin{array} { l } 8 \mathrm { X } _ { 1 } + 5 \mathrm { X } _ { 2 } \geq 80 \\3 \mathrm { X } _ { 1 } + 5 \mathrm { X } _ { 2 } \geq 60 \\\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } \geq 0\end{array}$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\hline 1 & & & & & \\\hline 2 & & & & & \\\hline 3 & & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & & \\\hline 4 & \text { Number to make: } & & & & \text { OBJ. FN. VALUE } \\\hline 5 & \text { Unit profit: } & & & & \\\hline 6 & & & & & \\\hline 7 & \text { Constraints: } & & & \text { Used } & \text { Available } \\\hline 8 & 1 & & & & 8 \\\hline 9 & 2 & & & & 80 \\\hline 10 & 3 & & & & 60 \\\hline\end{array}$$

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Definitions:

Retention of Earnings

The portion of net income that is retained by a company rather than distributed to its shareholders as dividends, often used for reinvestment.

Common Stock

Equity ownership in a corporation, giving holders voting rights and a share in the company's profits through dividends or stock appreciation.

Consumption Tax

A tax on the purchase of goods or services, levied at the point of sale.

Ad Valorem Tax

A tax based on the assessed value of an item, such as real estate or personal property, commonly used in property taxes.