Sullivan Algebra and Trigonometry: Section 12.9

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Sullivan Algebra and Trigonometry Section 12.9

• Objectives of this Section
• Set Up a Linear Programming Problem
• Solve a Linear Programming Problem

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A linear programming problem in two variables x
and y consists of maximizing (or minimizing) a
linear objective function
z Ax By, A and B are real numbers, not both 0
subject to certain constraints expressible as
linear inequalities in x and y.
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Begin by graphing each inequality. Find the
feasible region, that is, all the points in the
plane that satisfy all constraints.
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y -3x 16
Feasible Region
(0, 20/3)
(4, 4)
(0,0)
(16/3, 0)
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The maximum value of z is 24 and occurs at the
point (4, 4).
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Theorem Location of the Solution of a Linear
Programming Problem
If a linear programming problem has a solution,
it is located at a corner point of the graph of
the feasible points.
If a linear programming problem has multiple
solutions, at least one of them is located at a
corner point of the graph of the feasible points.
In either case, the corresponding value of the
objective function is unique.