Taco Loco Is Considering a New Addition to Their Menu $\text { Variable Cells }$

question 17

Multiple Choice

Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management.
Max R = 14Z + 13Y + 17X
subject to:
Beef   2Z + 3Y + 4X ? 28
Cheese  9Z + 8Y + 11X ? 80
Beans  4Z + 4Y + 2X ? 68
X,Y,Z ? 0
The sensitivity report from the computer model reads as follows:
$\text { Variable Cells }$
$\begin{array}{ccccccc}\hline \text { Cell } & \text { Name } & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Reduced } \\\text { Cost }\end{array} & \begin{array}{c}\text { Objective } \\\text { Coefficient }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \text { \$C\$4 } & \mathrm{Z} & 1.45 & 0 & 14 & 0.63 & 5.33 \\\hline \text { \$D\$4 } & \text { Y } & 8.36 & 0 & 13 & 8 & 0.56 \\\hline \text { \$E\$4 } & \mathrm{X} & 0 & -0.818 & 17 & 0.818 & 1 \mathrm{E}+30 \\\hline\end{array}$

$\text { Constraints }$
$\begin{array}{llccccc}\hline \text { Cell } & {\text { Name }} & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Shadow } \\\text { Price }\end{array} & \begin{array}{c}\text { Constraint } \\\text { R.H. Side }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \text { \$F\$6 } & \text { Beef } & 28 & 0.45 & 28 & 2 & 10.22 \\\hline \text { \$F\$7 } & \text { Cheese } & 80 & 1.45 & 80 & 46 & 5.33 \\\hline \text { \$FS8 } & \text { Beans } & 39.27 & 0 & 68 & 1 \mathrm{E}+30 & 28.73 \\\hline\end{array}$
-The optimal quantity of the three products and resulting revenue for Taco Loco is:

• A) 28 beef, 80 cheese, and 39.27 beans for $147.27
• B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27
• C) 1.45 Z, 8.36 Y, and 0 Z for $129.09
• D) 14 Z, 13 Y, and 17 X for $9.81

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Definitions:

Charged

A state of having an imbalance of electric charge, either positive or negative, which can result in electrostatic attraction or repulsion.

Electric Power

The rate, per unit time, at which electrical energy is transferred by an electric circuit, typically measured in watts.

Alternators

Alternators are electrical machines that convert mechanical energy into alternating current (AC) electrical energy, commonly used in vehicles and power generation.

Voltage Stack

A series arrangement of components or cells that results in a total voltage equal to the sum of the individual voltages.