Consider the following problem, where the value of c$1$

has not yet been ascertained.

Maximize Z $=$ c$1$x$1+$ x$2,$

subject to

x$1+$ x$2<=6$

x$1+2$x$2<=10$

and

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

Use graphical analysis to determine the optimal solution$($s$)$ for

$($x$1,$ x$2)$ for the various possible values of c$1(\backslash$infty $<$ c$1<\backslash$infty $).$