Consider the following linear programming problem.

Min	4A + 7B
s.t.
	1A + 4B		22
	2A + 1B		9
	3A + 1.5B		24
	2A + 6B		2
	A, B 0

(a)

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

at (A, B) =

(b)

Determine the amount of slack or surplus for each constraint.

slack for

1A + 4B 22

surplus for

2A + 1B 9

slack for

3A + 1.5B 24

surplus for

2A + 6B 2

(c)

Suppose the objective function is changed to max

5A + 2B.

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

at (A, B) =