I'm confused. I could swear you said LINEAR programming. The last time I checked, prod(f) would be nonlinear. That new math changes all the time though, so I might be wrong. :)
Use fmincon instead, because the problem is nonlinear, i.e., NOT linear. It is a minimization tool, as are all of those tools. So minimize -prod(f) instead.
And, since that product will almost surely end up having numerical problems, you will find yourself needing to minimize -sum(log(f)), but a minimizer of one is a minimizer of the other.
Finally, expect that to have numerical problems too, since some of those elements might occasionally go slightly negative, whereby the log of a negative number will be a problem. It would be a problem in the product anyway, since a sign change in the product will still be a problem.
So, expect this to be difficult to solve.
