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

question 38

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.
$$\begin{array}{l}\text { Formulation }\\\begin{array} { l l } \ { \text { Max } } & 10 \mathrm {~A} + 10 \mathrm {~B} + 10 \mathrm { C } \\\text { Subject to: } & \\& 3 \mathrm {~A} + \mathrm { B } + 5 \mathrm { C } \leq 300 \text { (constraint \#1) } \\& 2 \mathrm {~A} + 4 \mathrm {~B} \leq 400 \text { (constraint \#2) } \\& 4 \mathrm {~A} + 2 \mathrm {~B} + 3.5 \mathrm { C } \leq 200 \text { (constraint \#3) } \\& \mathrm { C } \geq 10 \text { (constraint \#4) } \\& \mathrm { A } , \mathrm { B } , \mathrm { C } \geq 0\end{array}\end{array}$$

-By how much would the profit contribution of product A has to increase before it will be profitable to produce A?

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Definitions:

Continuous Improvement

An ongoing effort to improve products, services, or processes through incremental and breakthrough improvements.

Core Processes

Fundamental business processes that are critical to an organization's operation and delivery of its products or services to customers.

Organisation's Mission

The fundamental purpose that defines an organization's core goals and directs its strategic planning.

Work Process

A series of actions or steps taken in order to achieve a particular end in a workplace.