Answer to Question #304542 in Operations Research for YAT

Question

Convert the following linear programming problem into dual

problem.

Maximise

Z = 22x1 + 25x2 +19x3

Subject to:

18x1 + 26x2 + 22x3 ≤ 350

14x1 + 18x2 + 20x3 ≥180

17x1 + 19x2 + 18x3 = 205

x1, x2, x3 ≥ 0

Answer 1

Solution:

All ≥ constraints can be converted to ≤ type by multiplying both sides by -1

 MAX Zx= 22x1+25x2+19x3

subject to

18x1+26x2+22x3≤350

-14x1-18x2-20x3≤-180

17x1+19x2+18x3=205

and x1,x2,x3≥0;

Since 3rd constraint in the primal is equality, the corresponding dual variable y3 will be unrestricted in sign.

Dual is (Solution steps of Dual by BigM method)

MIN Zy=350y1-180y2+205y3

subject to

18y1-14y2+17y3≥22

26y1-18y2+19y3≥25

22y1-20y2+18y3≥19

and y1,y2≥0;y3 unrestricted in sign