The computer solution is shown below.

$($a$)$ Identify the range of optimality for each objective function coefficient. $($If there is no upper or lower limit$,$ enter NO LIMIT.$)$

$($c$)$ Identify the range of feasibility for the right$-$hand$-$side values. $($If there is no upper or lower limit$,$ enter NO LIMIT.$)$

constraint $1$

constraint $2$

to

constraint $3$

to

$($d$)$ If the number of fan motors available for production is increased by $75,$ will the dual value for that constraint change? Explain.

Yes, the dual value will change because $75$ is greater than the allowable increase of $12.$

Yes, the dual value will change because $75$ is greater than the allowable increase of $45$

No$,$ the dual value will not change because $75$ is less than the allowable increase of $265.$

No$,$ the dual value will not change because there is no upper limit to how much the constraint can increase.