Use This Information,along with Its Associated Sensitivity Report,to Answer the Following

question 25

Multiple Choice

Use this information,along with its associated Sensitivity Report,to answer the following questions.
A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits.Production requirements for the products are shown in the following table.
$$\begin{array} { | c | c | c | c | } \hline \underline { \text { Product } } & \frac { \text { Material 1 } } { ( \mathrm { lbs } ) } & \frac { \text { Material 2 } } { ( \mathrm { lbs } . ) } & \text { Labor (hours) } \\\hline \underline { \underline { \mathrm { A } } } & \underline { 3 } & \underline { 2 } & \underline { 4 } \\\hline \underline { \mathrm { B } } & \underline { 1 } & \underline { 4 } & \underline { 2 } \\\hline \underline { \mathrm { C } } & \underline { 5 } & \underline { \text { none } } & \underline { 3.5 } \\\hline\end{array}$$
Material 1 costs $7 a pound,material 2 costs $5 a pound,and labor costs $15 per hour.Product A sells for $101 a unit,product B sells for $67 a unit,and product C sells for $97.50 a unit.Each week there are 300 pounds of material 1;400 pounds of material 2;and 200 hours of labor.The output of product A should not be more than one-half of the total number of units produced.Moreover,there is a standing order of 10 units of product C each week.
$$\begin{array}{l}\text { Formulation }\\\begin{array} { l l } \ { \text { Max } } & 10 \mathrm {~A} + 10 \mathrm {~B} + 10 \mathrm { C } \\\text { Subject to: } & \\& 3 \mathrm {~A} + \mathrm { B } + 5 \mathrm { C } \leq 300 \text { (constraint \#1) } \\& 2 \mathrm {~A} + 4 \mathrm {~B} \leq 400 \text { (constraint \#2) } \\& 4 \mathrm {~A} + 2 \mathrm {~B} + 3.5 \mathrm { C } \leq 200 \text { (constraint \#3) } \\& \mathrm { C } \geq 10 \text { (constraint \#4) } \\& \mathrm { A } , \mathrm { B } , \mathrm { C } \geq 0\end{array}\end{array}$$

-Suppose that the objective function coefficient for product C increases by $8.What impact will this have on the current values of the optimal solution?

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Definitions:

Cauda Equina

The cauda equina is a bundle of spinal nerves and spinal nerve rootlets below the end of the spinal cord, resembling a horse's tail, which distributes nerve roots to the lower limbs and pelvic organs.

Filium Terminale

The filium terminale is a slender filament of connective tissue that extends from the conus medullaris at the lower end of the spinal cord to the coccyx, anchoring the spinal cord in place.

Conus Medullaris

The tapered, lower end of the spinal cord, typically ending around the first lumbar vertebra.

Cervical Enlargement

A widened area of the spinal cord that supplies nerves to the shoulders, arms, and hands.