Find the dual of:

Maximize z=2x1+x2+3x3+4x4

subject to

4x1+2x2+5x3+5x4<=10

4x1+2x2+5x3+5x4>=15

3x1+5x2+4x3+x4>=8

3x1+5x2+4x3+x4<=15

x1+x2+x3+x4 = 20

x1,x2,x3,x4>=0

Is the dual for the above lp problem correct?

minimize z'=10w1-5w2-8w3+15w4+20w5

subject to

4w1-4w2-3w3+3w4+w5>=2

2w1-2w2-5w3+5w4+w5>=1

5w1-5w2-4w3+4w4+5w5>=3

5w1-5w2-w3+w4+w5>=4

w1,w2,w3,w4,w5>=0