You Have Been Given the Following Linear Programming Model and Excel

question 79

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?
$$\begin{array} { l l } \text { MAX: } & 4 X _ { 1 } + 3 X _ { 2 } \\\text { Subject to: } & 6 X _ { 1 } + 7 X _ { 2 } \leq 84 \\& X _ { 1 } \leq 10 \\& X _ { 2 } \leq 8 \\& X _ { 1 } , X _ { 2 } \geq 0\end{array}$$ $$\begin{array} { | c | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\hline 1 & & & & & \\\hline 2 & & & & & \\\hline 3 & & X _ { 1 } & \mathrm { X } _ { 2 } & & \\\hline 4 & \text { Number to make: } & & & & \text { OBJ. FN. VALUE } \\\hline 5 & \text { Unit profit: } & & & & \\\hline 6 & & & & & \\\hline 7 & \text { Constraints: } & & & \text { Used } & \text { Available } \\\hline 8 & 1 & & & & 84 \\\hline 9 & 2 & & & & 10 \\\hline 10 & 3 & & & & 8 \\\hline\end{array}$$

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Definitions:

Feldspar

Feldspar is a group of abundant rock-forming minerals that are major components of igneous, metamorphic, and sedimentary rocks, characterized by their silicate structure.

Quartz

A hard, crystalline mineral composed of silicon dioxide, widely distributed in many types of rocks and used in various industrial applications.

Granite

An igneous rock with a rough texture, primarily consisting of quartz, feldspar, and mica, often utilized in building projects.

Alcoholism

A chronic disease characterized by uncontrolled drinking and a preoccupation with alcohol, significantly affecting one's health, relationships, and responsibilities.