I $($MATH$-1324-$NO$4)$

Use the simplex method to solve the linear programming problem.

Maximize $z=10x_1+21x_2$

subject $to$: $12x_1+3x_{2}30$

$6x_1+x_{2}40$

$,3x_1+3x_{2}42$

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

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A$.$ The maximum is when $x_1=$dots,$x_2=$dots,$s_1=s_2=$ and $s_3=($Type integers or simplified fractions.$)$

B$.$ There is no maximum.

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