The supervisor of a manufacturing plant is trying to determine how many of two parts, Part $x$ and Part $Y,$ are to be produced per day. Each part must be processed in three

sections of the plant. The time required for the production along with the profit contribution for each part are given in the following table.

Time Required $($Minutes$/$Unit$)$

No more than $60$ units of Part $x$ and up to $70$ units of Part Y can be produced daily. The company already has orders for $30$ units of Part Y that must be satisfied. Develop

an LP model and solve for the optimal production quantities. Obtain the sensitivity report to answer the following questions.

a$.$ What is the amount of change in the objective function value if we increase the production quantity of Part Y by $1$ unit from the optimal solution? $($provide your answer

in numerical value only$)$

b$.$ If more time could be made available in Section $2,$ how much would the profit increase? $($provide your answer in numerical value only$)$

c$.$ If we increase the available hours for Section $1$ by $100$ units, what would be the resulting change in profit? $($provide your answer in numerical value only$)$The supervisor of a manufacturing plant is trying to determine how many of two parts, Part X and Part Y$,$ are to be produced per day. Each part must be processed in three sections of the plant. The time required for the production along with the profit contribution for each part are given in the following table.

Time Required $($Minutes$/$Unit$)$

Section $1$ Section $2$ Section $3$ Profit$/$Unit

Part X

$50$

$30$

$18$

$$2$

Part Y

$80$

$45$

$22$

$$3$

Available time $($minutes$)$

$3,600$

$2,500$

$1,200$

$$

No more than $60$ units of Part X and up to $70$ units of Part Y can be produced daily. The company already has orders for $30$ units of Part Y that must be satisfied. Develop an LP model and solve for the optimal production quantities. Obtain the sensitivity report to answer the following questions.

a$.$ What is the amount of change in the objective function value if we increase the production quantity of Part Y by $1$ unit from the optimal solution? $($provide your answer in numerical value only$)$

b$.$ If more time could be made available in Section $2,$ how much would the profit increase? $($provide your answer in numerical value only$)$

c$.$ If we increase the available hours for Section $1$ by $100$ units, what would be the resulting change in profit? $($provide your answer in numerical value only$)$