$4\mathrm{.}7-1.$ Reconsider Prob. $4\mathrm{.}6-1.$

$($a$)$ Follow the instructions for Prob. $4\mathrm{.}6-1$ in preparation for doing the following parts. $($If

you have previously solved Prob. $4\mathrm{.}6-1,$ simply refer back to that previous solution.$)$

$($b$)$ Using the Big $M$ method, construct the complete first simplex tableau for the Page $160$

simplex method and identify the corresponding initial $($artificial$)BF$

solution. Also identify the initial entering basic variable and the leaving basic variable.

I $($c$)$Continue from part $($b$)$ to work through the simplex method step by step to solve the

problem.

$4\mathrm{.}6-1.$ Consider the following problem.

Maximize $Z=2x_1+3x_2,$

subject to

$x_1+2x_{2}4$

$x_1+x_2=3$

and

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