Question

"Primal"
MAXIMIZE  Z = 12X1 + 18X2 +10X3
S.T.
                             2X1  + 3X2   + 4X3    <= 50
                              -X1  +  X2     +  X3    <= 0
                              0X1  -  X2 + 1.5X3    <= 0
                                 X1, X2, X3 >=0

1)
a)  Write the "Dual" of this problem.
b)  Write the "Dual of the Dual" of this problem.
For steps C & D, use the Generic Linear Programming spreadsheet or the software of your choice.  
(indicating the solution values and objective function value.)
c)  Solve the "Primal" problem.  (Find values of X1, X2, X3 and the Maximum Z)
d)  Solve the "Dual" problem. (Find values of Y1, Y2, Y3 and the Minimum Z*)

Answer 1

Solution:

We have,

Primal:

Maximize,

Subject to,

a.) Dual:

Minimize,

Subject to,

b) Dual of Dual:

Maximize,

Subject to,

c) Solution of 'Primal' problem

d) Solution of 'Dual' problem