How to find the maximum of sqrt((x-1)*(y-x))+sqrt((7-y)*(1-x))+sqrt((x-y)*(y-7)) for x=-2..3,
y=0..11 with Maple?
Here are a few unsuccessful attempts.
> Optimization:-Maximize(sqrt((x-1)*(y-x))+sqrt((7-y)*(1-x))+sqrt((x-y)*(y-7)),
x = -2 .. 3, y = 0 .. 11);
Error, (in Optimization:-NLPSolve) complex value encountered
> maximize(sqrt((x-1)*(y-x))+sqrt((7-y)*(1-x))+sqrt((x-y)*(y-7)), x = -2 .. 3, y = 0 .. 11);
Error, (in maximize) cannot minimize over a complex valued function
> DirectSearch:-GlobalOptima(sqrt((x-1)*(y-x))+sqrt((7-y)*(1-x))+sqrt((x-y)*(y-7)), {x >= -2, y >= 0, x <= 3, y <= 11}, maximize, tolerances = 10^(-14), evaluationlimit = 10^5);
[HFloat(2.6321248070712757),
[x = HFloat(0.0090), y = HFloat(0.0090)], 88]
