Consider the following linear program:

Min z $=8$ x$1,1+6$ x$1,2+7$ x$2,1+11$ x$2,2+13$ x$3,1+8$x$3,2$

s$.$t$.$ x$1,1+$ x$1,2<=300$

x$2,1+$ x$2,2<=400$

x$3,1+$ x$3,2<=500$

x$1,1+$x$2,1+$x$3,1>=225$

x$1,2+$x$2,2+$x$3,2>=315$

xi$,$j $>=0$

$($a$)(17\mathrm{.}5$ points$)$ Solve this problem using the greedy method.

$($b$)(4$ points$)$ Suppose that the objective coefficient on x$1$ changes from $8$ to $10,$ does this

change the optimal solution?

$($c$)(3\mathrm{.}5$ points If the demand of the second warehouse changes from $315$ to $400,$ how does

the optimal objective value change? Explain