Question

3. Problem 4-10 on p. 164: Find the optimal value of the objective function for the following problem by inspecting only its dual. (Do not solve the dual by the simplex method). Minimize z = 10x1 + 4x2 + 5x3 subject to 5x1 - 7x2 + 3x3 > 50 x1 > 0, x2 > 0, x3 0

Answer 1

Here im concept first in dyal form and then fund solution of dyal using inspection method answer is below thank you .

Dual of the given problem is let y be dual variable maximize wa soy subject to 542 10 = 932 -24547 y>4 34 55oys to and 320 Now we fins optimal solutions of these dual problem uning inspection me that 1. Here from these 3 constraint we observed that y>722 and us and also ">,0 dual problem reduce to maximize wasoy subject to ys 5 y>,0 As of us h is strangest constraint of all 3 constraints and we find maximum value so we false y=5. i optimal scluteas is y=5 and manimize wz 50(2) - Thank you