2x+3y = 10, отсюда
y = (1/3)*(10 - 2x).
Тогда
x*y = x*(1/3)*(10 - 2x) = (x/3)*(10 - 2x) = f(x).
f (x) = (10x/3) - (2x^2/3).
f '(x) = (10/3) - (4x/3),
(10/3) - (4x/3) = 0,
10 - 4x = 0,
x = 10/4 = 5/2 = 2,5. точка максимума
f(2,5) = f(5/2) = (5/2)*(1/3)*(10 - 2*(5/2)) = (5/6)*(10 - 5) = 5*5/6 = 25/6.
Ответ. 25/6.