Hi all.
I have a difficult mathematical problem to solve, please look at the
following data:
1 2 3 4
5 6
Isobuthane MTBE C5 C4
objective
A Density 0.775 0.78 0.89 0.8
0.79
B Sulfur 0.001 0.02 0 0.01
0.001
C MON 82 87 86 83
85

The excel table is like this one but with other 5 components (Caol,
Isobutilen, n-pentane, €¦€¦) and other 6 variables (viscosity, RON, cl point,€¦
) having 10 linear equations and 10 unknowns which is solvable, I solve for
all the equations applying ={mmult(minv(data coefficient),data)} (as a range
enter), but I got negative results (which was obvious) , but I can not take
out some material that was not there in the first place!!!.
My goal is to obtain the best problem solution, meaning that all material
amounts are positive and that they stick to the objective value the best they
can (I actually have limits for the objective values which could be iterated
to find the best solution).
Two premises are very important:
1) The materials used can be from 1 to 10 (I can eliminate n materials but
then I also need to eliminate n properties to have a" n x n" matrix), those
eliminated properties must be consider in the solution, meaning that I need
to have THE BEST SOLUTION whit them and without them.
2) No negative material amount can exist in the solution.
I'm aware that this is impossible to solve mathematically, but there MUST be
a way to solve it by iteration techniques.
Please note that I'm looking for the best possible solution and not the
mathematical only one solution.
There is another equation (material general balance) which is a+b+c+d+€¦.=
15000 (being 15000 the amount of materials' mix to be obtained, also is
flexible)
Any suggestions will be appreciated!
Thanks for your help