Linear Programming

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Linear Programming is a method to achieve the
best outcome (such as maximum profit or lowest
cost).

• Objective Function
• The linear function (equal sign) representing
  cost, profit, or some other quantity to be
  maximized of minimized subject to the
  constraints.
• Constraints
• A system of linear inequalities.

Feasible Region The solution to the system of
linear inequalities. That is, the set of all
points that satisfy all the constraints. Only
points in the feasible region can be
used. Corner Point A vertex of the feasible
region. Not every intersection of lines is a
corner point. The corner points only occur at a
vertex of the feasible region. If there is going
to be an optimal solution to a linear programming
problem, it will occur at one or more corner
points, or on a line segment between two corner
points.
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X t-shirts Y caps
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P 4x 3y
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8x 4y ? 800 x y ? 120
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Vertices (0, 0) (100, 0) (0, 120) (80, 40)
Maximize P 4x 3y
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Vertices (0, 0) (100, 0) (0, 120) (80, 40)
Maximize 0 4(0) 3(0) 400 4(100) 3(0) 360
4(0) 3(120) 440 4(80) 3(40)
Maximize Combination is 80 t-shirts and 40 caps
with a profit of 440