Hi, I really need some help on this! I've been working on the problem for about a week and I am not 100% sure that I found the right answer! Here's what I need to do:

1. Max L(x1,x2,x3,x4)=32.5x1+60x2+50x3+225x4

6 * x1 + 12 * x2 + 9 * x3 + 30 * x4 <= 9000

15 * x1 + 12 * x2 + 9 * x3 + 144 * x4 <= 30000

4 * x1 + 4 * x2 + 16 * x3 + 120 * x4 <= 16000

x1>=0 x2>=10 x3>=30 x4>=0

I have to solve this, but as you see x2>=10 and x3>=30, so here's what I did:

Min L(x1,x2,x3,x4)=32.5x1+60x2+50x3+225x4

6 * x1 + 12 * x2 + 9 * x3 + 30 * x4 <= 9000

15 * x1 + 12 * x2 + 9 * x3 + 144 * x4 <= 30000

4 * x1 + 4 * x2 + 16 * x3 + 120 * x4 <= 16000

X5-X2<=-10 -X5+X2>=10

X6-X3<=-30 -X6+X3>=30

x1>=0 x2>=0 x3>=0 x4>=0 x5>=0 x6>=0

I solved it and it looks fine!

2. Now I need to write the normal form and solve it:

Min L(x1,x2,x3,x4)=32.5x1+60x2+50x3+225x4

6 * x1 + 12 * x2 + 9 * x3 + 30 * x4+x7 = 9000

15 * x1 + 12 * x2 + 9 * x3 + 144 * x4+x8 = 30000

4 * x1 + 4 * x2 + 16 * x3 + 120 * x4+x9 = 16000

-X5+X2=10

-X6+X3=30

x1>=0 x2>=0 x3>=0 x4>=0 x5>=0 x6>=0

I did it and it looks OK

3. From the normal form I have to write the dual form and solve it. here's what I did:

6*y1+15*y2+4*y3>=32,5

12*y1+12*y2+4*y3+y4>=60

9*y1+9*y2+16*y3+y5>=50

30*y1+144*y2+120*y3<=255

-y4<=0

-y5=0

y1=0

y2=0

y3=0

y4=0

y5=0

What I get as answer from Excel Solver is: Solver could not find feasible solution! Is it possible? Could someone find any errors in my efforts? Am I right at all? I am completely lost now! Thanks for the help!