Aunt Anastasia Operates a Small Business: She Produces Seasonal Ceramic

question 26

Multiple Choice

Aunt Anastasia operates a small business: she produces seasonal ceramic objects to sell to tourists. For the spring, she is planning to make baskets, eggs, and rabbits. Based on your discussion with your aunt you construct the following table:
$$\begin{array} { l c c c c } \text { Product } & \begin{array} { c } \text { Mix/mold } \\\text { requirements (lb) }\end{array} & \begin{array} { c } \text { Kiln } \\\text { (units) }\end{array} & \begin{array} { c } \text { Paint \& Seal } \\\text { (hr) }\end{array} & \begin{array} { c } \text { Profit/product } \\\text { (\$) }\end{array} \\\hline \text { Baskets } & 0.500 & 1 & 0.250 & \$ 2.50 \\\text { Eggs } & 0.333 & 1 & 0.333 & \$ 1.50 \\\text { Rabbits } & 0.250 & 1 & 0.750 & \$ 2.00 \\\text { Capacity } & 20 \text { pounds } & 50 \text { units } & 80 \text { hours } & \\\hline\end{array}$$ Your aunt also has committed to make 25 rabbits for a charitable organization. Based on the information in the table, you formulate the problem as a linear program.
B = number of baskets produced
E = number of eggs produced
R = number of rabbits produced
MAX 2.5B + 1.5E + 2R
s.t.
0.5B + 0.333E + 0.25R ≤ 20
B + E + R ≤ 50
0.25B + 0.333E + 0.75R ≤ 80
R ≥ 25
The Excel solution and the answer and sensitivity report are shown below.
The Answer Report:
$\begin{array}{l}\text { Target Cell (Max) }\\\begin{array}{cccc}\hline \text { Cell } & \text { Name } & \begin{array}{c}\text { Original } \\\text { Value }\end{array} & \text { Final Value } \\\hline \$ C \$ 21 & \text { Profit } & 0 & \$ 112.5\end{array}\end{array}$

$\text { Adjustable Cells }$
$\begin{array}{cccc}\text { Cell } & \text { Name } & \begin{array}{c}\text { Original } \\\text { Value }\end{array} & \text { Final Value } \\\hline \$ C \$ 18 & \text { Baskets } & 0 & 25 \\\hline\$ C \$ 19 & \text { Eggs } & 0 & 0 \\\hline\$ C \$ 20 & \text { Rabbits } & 0 & 25\\\hline\end{array}$

$\text { Constraints }$
$\begin{array}{cccccc}\hline\text { Cell } & \text { Name } & \text { Cell Value } & \text { Formula } & \text { Status } & \text { Slack } \\\hline & & & & \text { Not } & \\\text { \$G\$13 } & \text { Mix/mold } & 18.75 & \text { \$G\$13<=\$F\$13 } & \text { Binding } & 1.25 \\\hline\text { \$G\$14 } & \text { Kiln } & 50 & \text { \$G\$14<=\$F\$14 } & \text { Binding } & 0 \\\hline & & & & & \text { Not } \\\text { \$G\$15 } & \text { Paint and Seal } & 25 & \text { \$G\$15<=\$F\$15 } & \text { Binding } & 55 \\\hline \text { \$G\$16 } & \text { Demand } & 25 & \text { \$G\$16>=\$F\$16 } & \text { Binding } & 0\end{array}$ The Sensitivity Report:
$\text { Adjustable Cells }$
$\begin{array}{ccccccc}\hline\text { Cell } & \text { Name } & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Reduced } \\\text { Cost }\end{array} & \begin{array}{c}\text { Objective } \\\text { Coefficient }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \$ C \$ 18 & \text { Baskets } & 25 & 0 & 2.5 & 1 \mathrm{E}+30 & 0.5 \\\hline \text { \$C\$19 } & \text { Eggs } & 0 & -1 & 1.5 & 1 & 1 \mathrm{E}+30 \\\hline \text { \$C\$20 } & \text { Rabbits } & 25 & 0 & 2 & 0.5 & 1 \mathrm{E}+30\end{array}$


$\text { Constraints }$
$\begin{array}{ccccccc}\hline\text { Cell } & \text { Name } & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Shadow } \\\text { Price }\end{array} & \begin{array}{c}\text { Constraint } \\\text { R.H. Side }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \$ G \$ 13 & \text { Mix/mold } & 18.75 & 0 & 20 & 1 \mathrm{E}+30 & 1.25 \\\hline \$ G \$ 14 & \text { Kiln } & 50 & 2.5 & 50 & 2.5 & 25 \\\hline \$ G \$ 15 & \text { Paint and Seal } & 25 & 0 & 80 & 1 \mathrm{E}+30 & 55 \\\hline \text { \$G } \$16 & \text { Demand } & 25 & -0.5 & 25 & 25 & 5 \\\hline\end{array}$
-Aunt Anastasia feels that her prices are too low, particularly for her eggs. How much would her profit have to increase on the eggs before it is profitable for her to make and sell eggs?

• A) $0.50
• B) $1.00
• C) $1.50
• D) $2.50

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Definitions:

De-ethnicization

The process by which a product or service sheds its ethnic identification and becomes appealing to a broader, multicultural market.

Ethnic Product

Goods that are specifically designed for, or associated with, a particular cultural or ethnic group.

High-context

A communication style wherein much of the information is understood from the context rather than stated explicitly in verbal or written form.

Gestures

Movements of the body, particularly the hands or head, used to express ideas or emotions.