Consider the following linear programming problem.

Min $6$A $+7$B

s$.$t$.$

$1$A $+4$B $<=22$

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

$3$A $+1\mathrm{.}5$B $<=24$

$2$A $+6$B $>=2$

A$,$ B $>=0$

$($a$)$

Find the optimal solution using the graphical solution procedure and the value of the objective function.

Correct: Your answer is correct.

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

Incorrect: Your answer is incorrect.

$($b$)$

Determine the amount of slack or surplus for each constraint.

slack for

$1$A $+4$B $<=22$

$14$

Correct: Your answer is correct.

surplus for

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

$1$

Incorrect: Your answer is incorrect.

slack for

$3$A $+1\mathrm{.}5$B $<=24$

$11\mathrm{.}5$

Incorrect: Your answer is incorrect.

surplus for

$2$A $+6$B $>=2$

$0$

Correct: Your answer is correct.

$($c$)$

Suppose the objective function is changed to max

$8$A $+3$B$.$

Find the optimal solution and the value of the objective function.

Incorrect: Your answer is incorrect.

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

Incorrect: Your answer is incorrect.