Consider the following linear program and answer the following questions.

Max $3A+4B$

$s.t.$

$-1A+2B7$

$1A+2B10$

$2A+1B15$

$A,B0$

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

$($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?

$S_1=$

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$S_2=$

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$S_3=$

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