maximize minimum-> 2 functions, 2 variables

Hi,

I have the following set of equations:

C1 = X1*X2*log(a) + X1*(1-X2)*log(b) >= T
C2 = X1*X2*log(c) + X2*(1-X1)*log(d) >= T

a,b,c,d are known constants. Now I want:

Max T over X1 and X2.

any ideas???

Thanks in advance.

Let me see if I get this straight. You want to find maxT while C's are always greater than T?

Then it must be maxT=min{C1,C2} for X1,X2. If your X's are defined throught the plane, just solve

http://www.artofproblemsolving.com/F...195b144370.gif

and compare the values to see which ones yield the minima. The min of these is maxT.

If though your variables belong in some region, then use Lagrange coefficients.