Minima Maxim/ax+by=c table

Your reasoning assumes that since the coefficient of y (16) is larger than the coefficient of x (15), increasing y should increase the total males. But x and y are not independent. They are tied by the constraint 29x + 33y = 5800. When y increases by 1, x must decrease by about 33/29 ≈ 1.14 to keep the total fixed. This drop in x reduces the male count more than the small gain from increasing y. So the expression 15x + 16y actually decreases as y increases, meaning the maximum occurs when y is as small as possible.