$5\mathrm{.}2-1$ Consider the following problem. Maximize $Z8x14x26x33x49x5,$ subject $tox12x23x33x4x5180(resource1)4x13x22x3x4x5270(resource2)x13x22x3x43x5180(resource3)$ and $xj0,j1,...,5.$ You are given the facts that the basic variables $in$ the optimal solution are $x3,x1,$ and $x5$ and that $1217.(a)$ Use the given information $to$ identify the optimal solution. $(b)$ Use the given information $to$ identify the shadow prices for the three resources. I $5\mathrm{.}2-2.*$ Work through the matrix form $of$ the simplex method step $by$ step $to$ solve the following problem.