Use the Simplex algorithm to find the optimum solution to the following LP$.$ Write standard form and use simplex table format. $($Write the simplex table for each iteration. Show the calculations, entering variable and leaving variable for each iteration clearly.$)$

maxz$=,3x_1+2x_2$

$s.t.2x_1+x_{2}100$

$,x_1+x_{2}80$

$,x_{1}40$

$,x_1,x_{2}0$