I have a job with I’m pretty stuck in the air. Following problem.

We have 300 Trucks. How many trucks of beer should be transported from each plant to each distribution center in order to minimize transportation costs?

Real variables:

X: Amount of trucks sent from production facility i (i = 1,2,3) to consumption center j (j = 1,2,3,4)

W: minimizing costs = W= 4000x1 + 5130x2 + 6500x3 + 8000x4 + 3520x5 + 4600x6 + 6900x7 + 7900x8 + 9900x9 + 6820y1 + 3880y2 + 6800y3

This is my programming in GAMS.

But I get variables with 0 even though I have defined psotive variables.

Positive Variable

x1,x2,x3,x4,x5,x6,x7,x8,x9,y1,y2,y3;

Free Variable

W;

Equation

obj, r1,r2,r3,r4,r5,r6,r7;

obj… W=e= (4000*x1 + 5130*x2 + 6500*x3 + 8000*x4 + 3520*x5 + 4600*x6 + 6900*x7 + 7900*x8 + 9900*x9 + 6820*y1 + 3880*y2 + 6800*y3)/300 ;

r1… x1+x2+x3+x4 =l= 75;

r2… x5+x6+x7+x8 =l= 125;

r3… x9+y1+y2+y3 =l= 100;

r4… x1+x5+x9 =e= 80;

r5… x2+x6+y1 =e= 65;

r6… x3+x7+y2 =e= 70;

r7… x4+x8+y3 =e= 85;

model Ej431 /all/;

solve Ej431 using LP minimizing W;

display X1.L, x2.l, x3.l, x4.l, x5.l, W.L;

Does anyone see my mistake?

Thank You very much