$[10]$ Consider the following problem, where the value of c$1$ has not yet been determined, : MAX z $=$ c$1$x$1+2$x$2$ Subject to $4$x$1+$ x$2<=12,$x$1-$x$2>=2,$a$)$ Determine binding and non$-$binding constraints.

b$)$ Use graphical analysis to determine the optimal solution$($s$)$ for $($x$1,$ x$2)$ for the

various possible c$1$ values.

c$)$ For which c$1$ value, does the problem have multiple optimal solutions?

d$)$ Calculate shadow prices for each constraint.