Question

Find two positive numbers such that the sum of the first and twice the second is 56 and whose product is a maximum

Answer 1

Let 
x-------> the first number
y-------> the second number
P-----> product

we know that
x+2y=56----------> 2y=56-x-----> y=28-0.5x------> equation 1
P=x*y----> equation 2

substitute equation 1 in equation 2
P=x*[28-0.5x]-----> P=28x-0.5x²

using a graph tool
see the attached figure
the vertex is the point (28,392)
that means
for x=28
the product is 392    (maximum) 
find the value of y
y=28-0.5x----> y=28-0.5*28----> y=14

the answer is
the numbers are 28 and 14