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IME 301-W10 - Methodology for Graphical Solutions

# IME 301-W10 - Methodology for Graphical Solutions -...

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Methodology for Graphical Solution of Linear Programming Problems 1. Given: Formulation (For example: the Ice Dream problem formulation) -Variable Definition -Objective Function (Z=.4X1+.3X2 / The profit to be maximized) -Constraints 2. Draw 2D Axis system, non-negative quadrant -Draw in constraints as equations (2/5X1 +1/2X2<=20 becomes 2/5X1 +1/2X2=20), and mark their feasible hyper-planes (“side” on which all point satisfy the constraint) 3. Determine feasible region -The intersection of all feasible hyper-plains 4. Draw objective function with a sensible number for Z -Pick a number that is easily devisable by the variable coefficients in the
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Unformatted text preview: objective function, and is within the graph’s scale 5. Shift the objective function-When looking for a maximum, shift the objective function parallel in the increasing direction until it hits the last point in the feasible region.-When looking for a minimum, shift the objective function parallel in the decreasing direction until it hits the last point in the feasible region. 6. Calculate the intersection-Use algebra (substitution) to calculate the last point in the feasible region, which is also the intersection of two constraint lines (2 equations 2 unknowns). Calculate the Z value at that point as well....
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