Question

Example 3.5-2 (Infinite Number of Solutions) Maximize z = 2xy + 4x2 subject to *'y + 2xy = 5 X1 + X2 5 4 *1,*220 Figure 3.9 demonstrates how alternative optima can arise in the LP model when the objec- tive function is parallel to a binding constraint. Any point on the line segment BC represents an alternative optimum with the same objective value z = 10. The iterations of the model are given by the following tableaus.

Answer 1

solve ( Using groaphical method) Maximum 72&4X2 subject to Xits x 25 Xot X2 ļ4 and & X2 70 X+ 2x₂ 25 1. Constraint Tread it as xi+ 5x₂5 0 5 + X2 2 4 Constroint Treat it as .X9+ , - 4 4 X2 4 9131) 2 AA 3 -X+2x225 X4 72 24

Extreme Point Coordmote (71, 82) objective function valve Z 2X + 4X2 10+ 4(0) = 0 0(0,0) A(410) B(311) ( (0,2.5) a (4)-1410) - 8 (3) +40) - 10 210) + 4(2.5) - 10 The maximum volue of the objective function =10 occurs at a extreme point. Hence problem has alternative optimal solutions and maxzz10