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 production manager has an additional 100 pounds of material 1.What impact will this have on the current optimal objective function value?
A)no change
B)a decrease of $100
C)an increase of $100
D)an increase of $200
E)an increase of $35

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 production manager has an additional 100 pounds of material 1.What impact will this have on the current optimal objective function value?
A)no change 
B)a decrease of $100 
C)an increase of $100 
D)an increase of $200 
E)an increase of $35

Quizplus · Accepted Answer

Looking at the sensitivity report, we see that the shadow price for Constraint #1 (material 1) is $10. This means that if we were to increase the amount of material 1 by 1 pound, the optimal objective function value (profit) would increase by $10. Since the production manager has an additional 100 pounds of material 1, we can assume that the optimal solution will use all 100 pounds to maximize profits. Therefore, the increase in profit would be $10 x 100 = $100. Hence, the answer is (C).

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