Collection S={ x,y are integers such that x,y>0 and x+y=28}

Let P be the product of x and y => P=xy

Now we have y=28-x => P=x.(28-x)

=28x-(x^2)

To find the largest value of the product P, differentiate P with respect to x and equate to zero.

We get 28-2x=0

=> 28=2x

=> x=14

thus y=28-x=14

So the largest product =x.y=196