$2.$ Consider the following problem. Assume that Xj is a product and that each constraint represents a manufacturing plant.

Maximize Z $=3$x$1+5$x$2+6$x$3,$

subject to

$2$x$1+$ x$2+$ x$3<=4$

x$1+2$x$2+$ x$3<=4$

x$1+$ x$2+2$x$3<=4$

x$1+$ x$2+$ x$3<=3$

and

x$1>=0,$ x$2>=0,$ x$3>=0.$

using the interior point method. Make the needed changes to the program and run it on SAS Studio.