Aunt Anastasia Operates a Small Business: She Produces Seasonal Ceramic

question 94

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 can obtain an additional 10 hours of kiln capacity free of charge from a friend. If she did this, how would her profits be affected?

• A) Profit would increase by $25.
• B) Profits would decrease by $25.
• C) Profits would decrease by $6.25.
• D) Cannot tell from the information provided.

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Definitions:

Land Dispute

Controversies or disagreements over the ownership, boundaries, or usage rights of land between parties.

Judicially Admitted

Statements or facts that have been acknowledged and accepted by a court as true and valid.

Partnership by Estoppel

A legal doctrine that treats a non-partner as a partner due to their actions or representations to third parties.

Statute of Frauds

A legal concept that requires certain types of contracts to be executed in writing and signed by the party to be charged with the contract.