Aunt Anastasia Operates a Small Business: She Produces Seasonal Ceramic

question 71

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's available hours for paint and seal have fallen from 80 hours to 60 hours because of other commitments. How will this affect her profits?

• A) Profits will increase by $30.
• B) Profits will decrease by $20.
• C) Profits will increase by $20.
• D) Profits will not change

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Definitions:

Marketing Program

A comprehensive plan that integrates all of the marketing efforts of a company, including advertising, sales, promotions, pricing, product development, and distribution.

Post-it Flag Highlighter

A writing instrument that combines the features of a highlighter pen with Post-it flags for marking and flagging documents.

Continuum

A continuous sequence or range where there are no clear divisions between adjacent elements but rather gradual differences or gradations.

Dichotomy

A division or contrast between two things that are represented as being entirely different.