Find two numbers whose sum is 23 and whose product is a maximum.

Let x = the first numberLet y = the second number x + y = 23 eq1 y = 23 - x

xy = Product eq2

Substitute eq1 into eq2. Lets get eq2 in terms of x.

Product = x (23 - x) Product = - x2 + 23x

we must find the vertex has coordinate (h, k). h = - b / 2a where:a = - 1b = 23

h = - 23 / - 2 = 11.5

x = 11.5

Substitute this value of x into eq1 to find y. y = 23 - xy = 23 - 11.5y = 11.5

The two numbers that will give the largest product possible are 11.5 and 11.5.