For the following problem, use graphical $sensitivity$ analysis $to$:

$a.$ Compute the optimality range $of{c}_1$ assuming that $c_{2}is$ constant. $(5$ points$)$

$b.$ Compute the optimality range $of{c}_2$ assuming that $c_{1}is$ constant. $(5$ points$)$

$c.$ Compute the unit worth $of$ resource $1(definedby$ first constraint$)$ and its feasibility range

$(HINT$: you can refer $to$ section $3\mathrm{.}6\mathrm{.}1of$ the textbook$)(10$ points$).$

Maximize

$z=4x_1+3x_2$

Subject $to$

$6x_1+4x_{2}30$

$x_1+2x_{2}8$

$2x_{2}7$

$x_1,x_{2}0$