$\backslash$table$[[,\backslash$table$[[$Number of$],[$Fans$]],\backslash$table$[[$Number of$],[$Cooling Coils$]],\backslash$table$[[$Manufacturing$],[$Time $($hours$)]]],[$Economy$,1,1,8],[$Standard$,1,2,12],[$Deluxe$,1,4,14]]$

programming model for the problem is as follows:

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

$s.t.$

$1E+1S+1D,240$ Fan motors

$1E+2S+4D,340$ Cooling coils

$8E+12S+14D,2,600$ Manufacturing time

$,$

The computer solution is shown below.

$\backslash$table$[[$Optimal Objective Value $=,18320\mathrm{.}00000],[\backslash$table$[[$Variable$,$Value,Reduced Cost$],[$E$,140\mathrm{.}00000,0\mathrm{.}00000],[$S$,100\mathrm{.}00000,0\mathrm{.}00000],[$D$,0\mathrm{.}00000,-24\mathrm{.}00000]],]]$

$\backslash$table$[[$Constraint$,$Slack$/$Surplus$,$Dual Value$],[1,0\mathrm{.}00000,31\mathrm{.}00000],[2,0\mathrm{.}00000,32\mathrm{.}00000],[3,280\mathrm{.}00000,0\mathrm{.}00000]]$

$\backslash$table$[[$Variable$,\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[$E$,63\mathrm{.}00000,12\mathrm{.}00000,15\mathrm{.}50000],[$S$,95\mathrm{.}00000,31\mathrm{.}00000,8\mathrm{.}00000],[$D$,135\mathrm{.}00000,24\mathrm{.}00000,$Infinite$],[,,,],[$Constraint$,$RHS$,$Allowable,Allowable$],[1,$Value,Increase,Decrease$],[2,240\mathrm{.}00000,70\mathrm{.}00000,70\mathrm{.}00000],[3,340\mathrm{.}00000,70\mathrm{.}00000,100\mathrm{.}00000],[,2600\mathrm{.}00000,$Infinite,$280\mathrm{.}00000]]$

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

$\backslash$table$[[E,$to$],[S,$to $$