Show that their product can be represented by the function

The product of two numbers is given by P= xy and the sum of the two numbers is given by S= x + y. If the sum of the two numbers is 80:

i) Show that their product can be represented by the function P=x(80-x ).

ii) Sketch a graph of the function P by placing P on the vertical axis, and x on the
horizontal axis. [Note: start at x= 0, and progress up to x= 80, using increments of 20]

iii) Determine the maximum product of the two numbers, and what are they both