I'm working on an interesting problem but stuck on a step that Mathematica fails on (no matter what angle I try to get at it from).
I'm attempting to find the symbolic maximum of this convex function (with respect to DY):
PArbNegDY[K0_, Y0_, S0_, DY_, DS_, \[Lambda]_] := -DY - ( K0 (DS + S0) (-1 + (Y0/(DY + Y0))^(1/\[Lambda])))/Y0 K0>0 && Y0>0 && S0>0 && DS>-S0 && 0<\[Lambda]<=1
So, I differentiated with respect to DY and am now trying to solve for it:
0 == -1 + (K0 (DS + S0) (Y0/(DY + Y0))^(-1 + 1/\[Lambda]))/((DY + Y0)^2 \[Lambda])
However, neither solve nor reduce give an answer (reduce runs forever). Any help would be greatly appreciated.