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

question 69

Short Answer

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:
$\text { Variable Cells }$
$\begin{array}{llccccc}\hline \text { Cell } & \text { Name } & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Reduced } \\\text { Cost }\end{array} & \begin{array}{c}\text { Objective } \\\text { Coefficient }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \text { \$C\$4 } & \mathrm{Z} & 1.45 & 0 & 14 & 0.63 & 5.33 \\\hline \text { \$D\$4 } & \text { Y } & 8.36 & 0 & 13 & 8 & 0.56 \\\hline \text { \$E\$4 } & \mathrm{X} & 0 & -0.818 & 17 & 0.818 & 1 \mathrm{E}+30 \\\hline\end{array}$

$\text { Constraints }$
$\begin{array}{llccccc}\hline {\text { Cell }} & {\text { Name }} & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Shadow } \\\text { Price }\end{array} & \begin{array}{c}\text { Constraint } \\\text { R.H. Side }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \text { \$F\$6 } & \text { Beef } & 28 & 0.45 & 28 & 2 & 10.22 \\\hline \text { \$F\$7 } & \text { Cheese } & 80 & 1.45 & 80 & 46 & 5.33 \\\hline \text { \$F\$8 } & \text { Beans } & 39.27 & 0 & 68 & 1 \mathrm{E}+30 & 28.73 \\\hline\end{array}$
-For humanitarian reasons, Taco Loco decides they would rather make product X than product Y. The dollar amount that they can both increase the price of Y and reduce the price of X by to accomplish this reversal of demand is ________.

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Definitions:

Poverty

The state of being extremely poor, where individuals or families lack the financial resources for basic living needs.

Success

The achievement of a goal or the accomplishment of an objective, often associated with personal or professional fulfillment.

Protective Factors

Conditions or attributes in individuals, families, communities, or the larger society that mitigate or eliminate risk and promote healthy development and well-being.

Resilient Children

Children who are able to recover quickly from difficulties or adapt well to significant challenges and stress.