# Linear programming

Consider the following linear programming problem:

Min x1 + 2x2

s.t.

x1 + 4x2 ≤ 21

2x1 + x2 ≥ 7

3x1 +1.5x2 ≤ 21

-2x1 + 6x2 ≥ 0

x1, x2 ≥ 0

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

b. Determine the amount of slack or surplus for each constraint.

c. Suppose the objective function is changed to max 5x1 + 2x2. Find the optimal solution and the value of the objective function.

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