GRAPHICAL SENSITIVITY ANALYSIS $(20$ points$)$

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 $1($defined by first constraint$)$ and its feasibility range

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

Maximize

$z=4x_1+3x_2$

$6x_1+4x_{2}30$

$x_1+2x_{2}8$

$2x_{2}7$

$x_1,x_{2}0$