The answer should be around 15.7, i.e., function h is maximized at around x=15.7, I don't know why my computer/maple is having a hard time with it.
f := proc (a, b, k) options operator, arrow; (sum(exp(-x)*x^m/(m!), m = a .. b))^k end proc;
h := f(0,0,82)*f(1,3,49)*f(4,6,47)*f(7,10,47)*f(11,15,57)*f(16,20,40)*f(21,25,38)*f(26,35,52)*(1-f(0,35,1))^91;
thanks in advance!