The following linear program model is used to optimize the production of four products $,x_2,x_3$ and $x_4),$ with two different manufacturing processes and two different material requirements.

Max $Z=$$$48x_1+$$$52x_2+$$$57x_3+$$$60x_4(Total$ profit$)$

$s.t.4x_1+2\mathrm{.}1x_2+2\mathrm{.}6x_3+3\mathrm{.}9x_{4}500(Process1)$

$,3\mathrm{.}5x_1+4\mathrm{.}6x_2+3\mathrm{.}5x_3+1\mathrm{.}9x_{4}600(Process2)$

$,15x_1+21x_2+19x_3+22x_{4}3500(MaterialA)$

$,7\mathrm{.}5x_1+11\mathrm{.}5x_2+9\mathrm{.}5x_3+10\mathrm{.}6x_{4}1600(MaterialB)$

$,x_1,x_2,x_3,x_{4}0,$

The linear program model is solved using Excel Solver and sensitivity reports are given as below:

Adjustable Cells

$\backslash$table$[[$Cell$,$Name,$\backslash$table$[[$Final$],[$Value$]],\backslash$table$[[$Reduced$],[$Cost$]],\backslash$table$[[$Objective$],[$Coefficient$]],\backslash$table$[[$Allowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[$$B $$15,$Product $1,29\mathrm{.}10,0,48,25\mathrm{.}35,1\mathrm{.}68],[$$C$$15,$Product $2,0,-17\mathrm{.}02,52,17\mathrm{.}02,1E+30$