What is the easiest way to minimize (or maximize) a function of many variables, if each variable can only take on one of two known values (a miminum or a maximum)?

The overall equation I'm trying to minimize (or maximize) is: V = (1+a/b)+a*c+d*(1/e + f + 1/g + h + 1/i + j - k - l - m) where all the variables can have one of two possible values (which are known). Is there an easy way to solve this problem? Would the optimization toolbox be useful or overkill since the constraints on each variable are pretty straightforward?

Edit: I also need to know which values for each variable produced the result.

[dpb]

Can the sign change between the two states? If not it seems straightforward examination should solve it...

Answer 1

[Steven Lord]

For a problem this small (2^13 = 8192 combinations), brute force. Use NDGRID to generate all combinations of the values, evaluate the function for all the combinations, call MAX or MIN with two outputs.

[Henry]

Will this method allow me to extract which values for each variable produced the result?

[Steven Lord]

Take a look at the second output from MAX.