The linear programming model for the problem is as follows:

Max $63E+95S+135D,$

$s.t.1E+1S+1D,$

$,1E+2S+260$ Fan motors

$,8E+125+14D,<mn\; id="EditorElement\_2958089">2</mn><mn\; id="EditorElement\_2958090">5</mn><mn\; id="EditorElement\_2958091">0</mn><mn\; id="EditorElement\_2958092">0</mn>$ Cooling coils

$,$

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.$)$

$E$

$S$

$]$ to

D

I to

$($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 $|$

to

$($d$)$ If the number of fan motors available for production is increased by $35,$ will the dual value for that constraint change? Explain.

Yes, the dual value will change because $35$ is greater than the allowable increase of $12.$

Yes, the dual value will change because $35$ is greater than the allowable increase of $5.$

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

No$,$ the dual value will not change because $35$ is less than the allowable increase of $265.$