Maximizing functions with Which statements

Question

I'd like to be able to find the maximum value that my Capex function (see below) generates. This is a fairly simple function so I could just add it up but I have more complex functions of a similar form that I'll need to maximize.

Capex[romSize_, CCSPsize_, washRate_, miningRate_] :=
Module[{val, rom = romSize, CCSP = CCSPsize, wash = washRate},
val = 0;
Which[CCSP > 500, val = val - 100];
Which[rom >= 200 && rom < 300, val = val - 5, rom >= 300, 
 val = val - 10];
Which[wash >= 1300 && wash < 1500, val = val - 10, wash >= 1500, 
val = val - 20];
Which[miningRate >= 5.5 && miningRate < 5.7, val = val - 10, 
miningRate >= 5.7, val = val - 20];
Return[val]
];

The problem I have is that because it contains Which statements the Maximize function doesn't seem to work. I could spam the Capex function with values in the domain and pick the largest value but I was hoping Mathematica had some functionality to make it a little easier, kind of like Goal Seek in Excel.

An example of a simple maximize call would be

Maximize[{Capex[x, 600, 1500, 6], 120 <= x <= 300}, {x}]

The max value of -240 is correct but x=300 is not

Answer 1

Since you're not using Which for more complex constructs or using a "default value", I suggest discarding the Which construct and instead adopting a far simpler approach to defining your Capex function:

capex[rom_, CCSP_, wash_, mining_] :=
    -100 ( CCSP   >  500                 ) +
    -5   ( rom    >= 200  && rom < 300   ) +
    -10  ( rom    >= 300                 ) +
    -10  ( wash   >= 1300 && wash < 1500 ) +
    -20  ( wash   >= 1500                ) +
    -10  ( mining >= 5.5  && mining < 5.7) +
    -20  ( mining >= 5.7                 ) /. {True -> 1, False -> 0}

or as J. M. notes, using Boole and Dot:

capex[rom_, CCSP_, wash_, mining_] := 
    {-100, -5, -10, -10, -20, -10, -20}.Boole[{CCSP > 500, 200 <= rom < 300, 300 <= rom, 
         1300 <= wash < 1500, 1500 <= wash, 5.5 <= mining < 5.7, 5.7 <= mining}]

You can verify that the above and your function return the same value for the same input.