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

question 20

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

$\text { Constraints }$
$\begin{array}{llccccc}\hline \text { Cell } & {\text { Name }} & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Shadow } \\\text { Price }\end{array} & \begin{array}{c}\text { Constraint } \\\text { R.H. Side }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \text { \$F\$6 } & \text { Beef } & 28 & 0.45 & 28 & 2 & 10.22 \\\hline \text { \$F\$7 } & \text { Cheese } & 80 & 1.45 & 80 & 46 & 5.33 \\\hline \text { \$FS8 } & \text { Beans } & 39.27 & 0 & 68 & 1 \mathrm{E}+30 & 28.73 \\\hline\end{array}$
-Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix?

• A) 26 to 38.22 pounds
• B) 27.55 to 28.45 pounds
• C) 17.78 to 30 pounds
• D) 12.22 to 28 pounds

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