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Unformatted text preview: Chapter 3.3: Solving Linear Programming Problems • Any solution to a linear programming problem must satisfy all in equalities in the set of constraints. • Graphically, this means that any point ( x,y ) that is a solution to the linear programming problem must be inside the feasible region. • Let us now examine the objective function. • Consider the objective function P = x + y . • This objective function describes a family of parallel lines, called iso profit lines : • For example, when P = 0, the objective function is the line 0 = x + y : • When P = 5, the objective function is the line 5 = x + y : • Notice that as the value of the objective function increases, so does the yintercept. 1 • Now let us consider the following linear programming problem. We will maximize this objective function, subject to the following constraints: x + y ≥ 2 x + y ≥ 5 x ≥ y ≥ y ≤ 8 • Here is a graph of the feasible region: • Putting together the ideas we’ve learned so far: 1. If an isoprofit line contains a point which is a solution, then the isoprofit line must intersect with the feasible region, and 2. To maximize, we need to find the isoprofit line with yintercept as large as possible, which also intersects the feasible region....
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This note was uploaded on 02/05/2011 for the course MATH 377 taught by Professor Stephenlang during the Spring '11 term at University of Victoria.
 Spring '11
 stephenlang
 Calculus, Linear Programming, Inequalities

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