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:

Production Methods

Techniques and processes used in the creation of goods or services, encompassing everything from materials selection and use of technology to labor and manufacturing practices.

Management Decisions

Choices or judgments made by the management of an organization regarding its operations, strategy, and resource allocation.

Seniority-Based

A system or practice where decisions on promotions, layoffs, and benefits are made based on the length of an employee's service within an organization.

Union-Mandated

Requirements or actions imposed by labor unions, often through collective bargaining or union regulations, that employers must follow.