This example is Mary's radiation therapy problem. Write an artificial version of this problem and find the initial solution for the original problem with big M method via Simplex.

Radiation Therapy Example

Minimize

Z$=0\mathrm{.}4$x$1+0\mathrm{.}5$x$2,$

subject to

$0\mathrm{.}3$x$1+0\mathrm{.}1$x$2<=2\mathrm{.}7$

$0\mathrm{.}5.$x$1+0\mathrm{.}5$x$2=6$

$0\mathrm{.}6$x$1+0\mathrm{.}4$x$2>=6$

and

X$1>=0,$

X$2>=0.$

solve this