Consider the following linear program and answer the following questions.Consider the linear program below and answer the following.

Min $10A+7B$

$s.t.$

$,2A+1B13$

$,1A+1B11$

$,1B4$

$,A,B0$

$($a$)$ Write the problem in standard form.

Min

s$.$t$.$

$2A+1B+$

$1A+1B$

$0A+1B$

$A,B,S_1,S_2,S_{3}0$

Max$3A+4B$

$s.t.$

$-1A+2B7$

$1A+2B13$

$2A+1B15$

$A,B0$

$($a$)$ Write the problem in standard form.

Max$3A+4B+({|}_{})S_1+()S_2+({|}_{})S_3$

$s.t.$

$-1A+2B+$

$1A+2B$

$+$

$=13$

$2A+1B$

$+$

$=15$

$A,B,S_1,S_2,S_{3}0$

$=7$

$=13$

$+,=15$

$0$

$($b$)$ Solve the problem using the graphical solution procedure.

$($c$)$ What are the values of the three slack variables at the optimal solution?

$S_1=$

$S_2=$

$S_3=$