Consider the linear program:

Max		3A	+	4B
s.t.
		-A	+	2B		8	(1)
		A	+	2B		12	(2)
		2A	+	B		16	(3)
				A, B		0

Write the problem in standard form. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) If your answer is zero, enter 0. If the constant is "1" it must be entered in the box.

MaxMin	fill in the blank 2 A	+	fill in the blank 3 B	+	fill in the blank 4 S1	+	fill in the blank 5 S2	+	fill in the blank 6 S3
s.t.
	fill in the blank 7 A	+	fill in the blank 8 B	+	fill in the blank 9 S1					=	fill in the blank 11
	fill in the blank 12 A	+	fill in the blank 13 B			+	fill in the blank 14S2			=	fill in the blank 16
	fill in the blank 17 A	+	fill in the blank 18 B					+	fill in the blank 19S3	=	fill in the blank 21
									A, B, S1, S2, S3	=	fill in the blank 23

Select the correct graph that shows the optimal solution for the problem.

(i)		(ii)
(iii)		(iv)

Graph (i)

Graph (ii)

Graph (iii)

Graph (iv)

What are the values of the three slack variables at the optimal solution? If required, round your answers to one decimal place. If no entry is required, enter "0".

S1 =
S2 =
S3 =