Question

Find the dual problem for each of the following primal problems.

a): min z=6x1+8x2 st: 3x1+x2>=4 5x1+2x2>=7 x1,x2>=0

b): max z=8x1+3x2-2x3 st: x1-6x2+x3>=2 5x1+7x2-2x3=-4 x1<=0,x2<=0,x3 unrestricted

Answer 1

b) Given primal problem is :

Here we see that the primal variable x₃ is unrestricted in sign and the second constraint is an equation.

First of all let us rewrite the problem in its equivalent form with all positive variables by writting x₃ = x₃'-x₃'' as

Now we recast these in our required standard form as

Hence the dual problem is given by

i.e.,

This can be written again as