formulating a linear programming model and solving using Excel

Please see the attached file for the complete solution.
First, the model is:

Let a, b, c, d, e, f, g, h and i be values of cells 1-9 respectively.

We want minimize Z=6a+9b+7c+12d+3e+5f+4g+8h+11i

Subject to:

a+b+c<=130
d+e+f<=70
g+h+i<=100
a+d+g<=80
b+e+h<=110
c+f+i<=60

Second, we run the model in the excel. (Please see the attached file).

The solution is a=0, b=20, c=60, d=0, e=70, f=0, g=80, h=20 and i=0

and minimum value of Z=1290.

variables a b c d e f g h i constant
objective 6 9 7 12 3 5 4 8 11 condition
condition coefficient 1 1 1 0 0 0 0 0 0 130 80
0 0 0 1 1 1 0 0 0 70 70
0 0 0 0 0 0 1 1 1 100 100
1 0 0 1 0 0 1 0 0 80 80
0 1 0 0 1 0 0 1 0 110 110
0 0 1 0 0 1 0 0 1 60 60
solution to a 0
solution to b 20
solution to c 60
solution to d 0
solution to e 70
solution to f 0
solution to g 80
solution to h 20
solution to i 0
solution to objective 1290

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