Q$2.$ Consider the following LP problem:

Maximize $4x_1+2x_2+3x_3$

Subject $to$: $0\mathrm{.}1x_1+0\mathrm{.}25x_{2}40$

$0\mathrm{.}22x_1+0\mathrm{.}3x_2+0\mathrm{.}4x_{3}100$

$x_1,x_2,x_{3}0$

$($a$)$ Solve the problem using the simplex algorithm and list the binding and non$-$binding constraints with reasoning

$($b$)$ Calculate the revised values of decision variables and objective function if the right$-$hand side of the first constraint is reduced by $10$ units and the second constraint is increased by $10$ units.

$($c$)$ Calculate the revised values of decision variables and objective function if the right$-$hand side of the second constraint is decreased by $50$ units.

Points: $5+2\mathrm{.}5+2\mathrm{.}5$