15) Find two positive numbers x and y such that their sum is 35 and the product
is a maximum.
It is given that
x + y = 35 , x = 35 - y
and is maximum
Therefore,
Now,
Now,
Hence, y = 35 is the point of minima
Hence, y= 0 is neither point of maxima or minima
Hence, y = 25 is the point of maxima
x = 35 - y
= 35 - 25 = 10
Hence, the value of x and y are 10 and 25 respectively