Graphical Sensitivity Analysis

Sensitivity Analysis Source: Introduction to Management Science 10 e, Anderson Sweeney Williams  type 1 Max s.t. 5x1 + 7x2 x1 < 6 2x1 + 3x2 < 19 x1 + x2 < 8 x1, x2 > 0 x2 8 7 6 5 4 3 2 1 x1 + x2 < 8 Max 5x1 + 7x2 x1 < 6 Optimal: x1 = 5, x2 = 3, z = 46 2x1 + 3x2 < 19 x1 1 2 3 4 5 6 7 8 9 10 x2 8 7 6 5 4 3 2 1 5 5 Feasible Region 1 1 1 2 3 4 4 4 3 3 2 2 5 6 7 8 9 10 x1 Example 1 deviate of Optimality for c1 The boldness of meat of the objective intimacy draw and quarter is -c1/c2. The slope of the first back constraint, x1 + x2 = 8, is -1 and the slope of the second binding constraint, x1 + 3x2 = 19, is -2/3.

adventure the range of values for c1 (with c2 staying 7) such that the objective function line slope lies between that of the two binding constraints: -1 < -c1/7 < -2/3 Multiplying through by -7 (and reversing the in touch onities): 14/3 < c1 < 7 Example 1 Range of Optimality for c2 Find the range of values for c2 ( with c1 staying 5) such that the objective function line slope lies between that of the two binding constraints: -1 < -5/c2 < -2/3 Multiplying by -1: Inverting, Multiplying by 5: 1 > 5/c2 > 2/3 1 < 5 < c2/5 < 3/2 c2 < 15/2 Right-Hand Sides The improvement in the value of the optimal solution per unit increase in the right-hand side is called the dual price. The range of feasibility is the range over which the dual price is applicable. As the RHS increases, other constraints will become binding and limit the change in the value of the objective function.  double Price Graphically, a dual price is determined by adding +1 to the right hand side value in enquire and then resolving for the optimal solution in impairment of the same two binding constraints. The dual price is equal to the difference in the values of the objective functions between the bracing and original problems. The dual price for a nonbinding constraint is 0. A negative dual price indicates that the objective function will... If you compulsion to get a full essay, order it on our website: Orderessay

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