Consider the linear program minimize $-55x_1-45x_2$

subject $to4x_1+6x_{2}210,$

$x_1+3x_{2}90,$

$5x_1+8x_{2}600,$

$x_{1}0,x_{2}0.$

$($a$)$ Compute the first two iterates of the predictor$-$corrector primal$-$dual interior point method applied to the linear program above using the initial point generation method in Section $4\mathrm{.}5\mathrm{.}1.$ Use a tolerance of $={10}^{-6}.$

$($b$)$ Use the MATLAB function PD$\_$InteriorPoint in Section $6\mathrm{.}5$ to solve

the linear program above. Summarize the iterations in tables showing for each iteration the primal values, dual values, objective values, and residual values.

$($c$)$ Solve the linear program by using the MATLAB linprog function and verify the solution from $($b$).$