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?
A)No change.
B)Current solution will change.
C)Solution will become infeasible.
D)Solution will become unbounded.
E)Not enough information is provided.

Question

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?
A)No change. 
B)Current solution will change. 
C)Solution will become infeasible. 
D)Solution will become unbounded. 
E)Not enough information is provided.

Quizplus · Accepted Answer

If the objective function coefficient for product C increases, its value will be more than 10, which is the minimum amount required. Increase in the value will only increase profits, and therefore, the optimal solution values for products A and B will remain the same, and the optimal value will increase.

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