Min $6$x$1+9$x$2($cost$)$

S$.$T$.$

x$1+2$x$2<8-----$constraint $1$

$10$ x$1+7\mathrm{.}5$ x$2>30----$constraint $2$

x$2>2------$constraint $3$

x$1,$ x$2>0$

a$.$ What is the optimal solution including the optimal value of the objective function?

b$.$ Suppose the unit cost of is x$1$decreased to $$4.$ Is the above solution still optimal? What

is the value of the objective function when this unit cost is decreased to $$4?$

c$.$ How much can the unit cost of x$2$ be decreased without concern for the optimal solution

changing?

d$.$ If the right hand side of constraint $3$ is increased by $1,$ what will be the effect on objective

function?