Problem $1$:

This report presents the result of a linear program to determine the optimal product mix between four

possible products, Gears A$,$ B$,$ C and D$,$ which are proposed to be made using the following resources:

Drilling Hours, Milling Hours, Lathe Hours and Inspection Hours. The coefficients of the objective

function represent the profit to be made from the manufacture of each type of gear.

$($a$)$ What is the profit represented by the objective function?

$($b$)$ What is the production plan shown by this sensitivity report?

$($c$)$ Which constraints are binding? Which are non$-$binding?

$($d$)$ What is the range over which the OFC associated with Gear C can change without changing the

production plan indicated by this sensitivity report?

$($e$)$ What is the range over which the quantity of Lathe Hours could change without changing the

combination of binding constraints?

$($f$)$ Does this sensitivity report indicate the presence of multiple optima? How do you know?

$($g$)$ After the production, how many hours remain in the Milling department?

$($h$)$ After the production, how many hours remain in the Drilling department?

$($i$)$ What would be the impact to the production plan and profit if the $OF{C}_{\text{G}\text{e}\text{a}\text{r}}$A were to change to

$$20?$

$($j$)$ What would be the impact to the production plan and profit if the $OF{C}_{\text{G}\text{e}\text{a}\text{r}B}$ were to increase by

$$1?$

$($k$)$ What would be the impact to the production plan and profit if the $OF{C}_{\text{G}\text{e}\text{a}\text{r}}C$ were to change to

$$19?$

$(1)$ What would be the impact to the production plan and profit if the $OF{C}_{\text{G}\text{e}\text{a}\text{r}}D$ were to increase by

$$4?$