Question

Find two positive real numbers where the sum of the first number and twice the second is 36. Find the two numbers that maximize the product.

Answer 1

Step-by-step explanation:

Let the first number be x

Let the second number be y

The sum of the first number and twice of the second number is 36

Mathematically,

x + 2y = 36

Isolate x

x = 36 - 2y

Since the product of the numbers is x * y

Therefore, x * y = (36 - 2y) * y

36y - 2y^2

To maximixe, we need to differeentiate

36 - 4y = 0

Collect the like terms

36 = 0 + 4y

36 = 4y

Isolate y by dividing both sides by 4

36/4 = 4y / 4

y = 9

Find x

x = 36 - 2y

x = 36 - 2(9)

x = 36 - 18

x = 18

Therefore, x = 18 and y = 9