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Chapter 3 Linear programming and sensitivity analysis Example /1 • • • • Min Z= 6X1+3X2 S.t 2X1+4X2>=16 4X1+3X2>=24 • Solve the linear programming model using the Graphical method to found the value of X1,X2, and Z. Answer of Example /1 Example /2 • • • • • • • • • Consider the following linear program: MAX Z = 60A + 50B s.t. 10A + 20B ≤ 200 8A + 5B ≤ 80 A≥2 B≥5 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z. Answer of Example /2 Example /3 • • • • • • • • Consider the following minimization problem: Min z = x1 + 2x2 s.t. x1 + x2 ≥ 300 2x1 + x2 ≥ 400 2x1 + 5x2 ≤ 750 x1, x2 ≥ 0 Which constraints are binding at the optimal solution Answer of Example 3 Assignment of chapter 3 Maximize Z= x1 + x2 subject to x1 <=7 X1+ 5x2 <=5 X1,X2>=0 What is the value of Z 1. If Coefficient (OFC)of X1 change from 1 to 3? 2. If the parameter of X2 in constraint 1 change to 3? 3. If the parameter of X1 in constraint 2 change to 2?