Question: Consider the following linear programming problem. Min 2 A + 3 B s.t. 1 A + 4 B 21 2 A + 1 B 7

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.

= (BLANK) at (A, B) = (BLANK)

(b)

Determine the amount of slack or surplus for each constraint.

slack for 1A + 4B 21 = (BLANK)

surplus for 2A + 1B 7 = (BLANK)

slack for 3A + 1.5B 21 = (BLANK)

surplus for 2A + 6B 0 = (BLANK)

(c)

Suppose the objective function is changed to max

5A + 2B.

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

= (BLANK) at (A, B) = (BLANK)

****all "(blanks)" are where boxes for answers go

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