The following linear program model is used to optimize the production of four products $($X$1,$

X$2,$ X$3$ and X$4),$ with two different manufacturing processes and two different material

requirements.

Max Z $=$ $$48$X$1+$ $$52$X$2+$ $$57$X$3+$ $$60$X$4($Total profit$)$

s$.$t$.4$X$1+2\mathrm{.}1$X$2+2\mathrm{.}6$X$3+3\mathrm{.}9$X$4500($Process $1)$

$3\mathrm{.}5$X$1+4\mathrm{.}6$X$2+3\mathrm{.}5$X$3+1\mathrm{.}9$X$4600($Process $2)$

$15$X$1+21$X$2+19$X$3+22$X$43500($Material A$)$

$7\mathrm{.}5$X$1+11\mathrm{.}5$X$2+9\mathrm{.}5$X$3+10\mathrm{.}6$X$41600($Material B$)$

X$1,$ X$2,$ X$3,$ X$40$