Consider the following linear program and answer the following questions.

Max $3$A $+4$B

s$.$t$.$

$1$A $+2$B $<=7$

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

$2$A $+1$B $<=16$

A$,$ B $>=0$

$($a$)$

Write the problem in standard form.

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

Correct: Your answer is correct.

S$1+$

Correct: Your answer is correct.

S$2+$

Correct: Your answer is correct.

S$3$

s$.$t$.$

$1$A $+2$B $+$

Correct: Your answer is correct.

$=7$

$1$A $+2$B $+$

Correct: Your answer is correct.

$=12$

$2$A $+1$B $+$

Correct: Your answer is correct.

$=16$

A$,$ B$,$ S$1,$ S$2,$ S$3$

$?$

$0$

$($b$)$

Solve the problem using the graphical solution procedure.

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

Incorrect: Your answer is incorrect.

$($c$)$

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

S$1$

$=$

$0$

Incorrect: Your answer is incorrect.

S$2$

$=$

$0$

Correct: Your answer is correct.

S$3$

$=$

$0$

Correct: Your answer is correct.