Consider the following linear programming problem.
Min 4A + 5B
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
7A + 3B.
Find the optimal solution and the value of the objective function.
at (A, B) =