Consider the following linear program and answer the following questions.

Max $3$A $+4$B

s$.$t$.$

$1$A $+2$B $<=9$

$1$A $+2$B $<=11$

$2$A $+1$B $<=12$

A$,$ B $>=0$

$($a$)$

Write the problem in standard form.

Max $3$A $+4$B $+$

S$1+$

S$2+$

S$3$

s$.$t$.$

$1$A $+2$B $+=9$

$1$A $+2$B $+=11$

$2$A $+1$B $+=12$

A$,$ B$,$ S$1,$ S$2,$ S$30$

$($b$)$

Solve the problem using the graphical solution procedure.

$($A$,$ B$)=$

$($c$)$

What are the values of the three slack variables at the optimal solution?

S$1$

$=$

S$2$

$=$

S$3$

$=$