Use inequality of arithmetic and geometric means for three variables.


It says  (see this Wikipedia article  https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means) :



    For any 3 non-negative numbers  a, b  and  c


         >= ,

        and inequality becomes the equality if and only if  a = b = c.



In your case, it means that if  a + b + c = 15,  then  a*b*c has the maximum value of 5*5*5 = 125  when  a = b = c = 5.