3-3 - Chapter 3.3 Solving Linear Programming Problems Any...

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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 y -intercept. 1
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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 0 y 0 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 y -intercept as large as possible, which also intersects the feasible region.
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