Consider the following linear programming problem.

Min	2A + 3B
s.t.
	1A + 4B		21
	2A + 1B		7
	3A + 1.5B		21
	2A + 6B		0
	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 21 =

surplus for 2A + 1B 7 =

slack for 3A + 1.5B 21 =

surplus for 2A + 6B 0 =

(c) Suppose the objective function is changed to max 7A + 3B. Find the optimal solution and the value of the objective function.

________ at (A, B) = (_______)