Expert: Paul Klarreich - 12/9/2007

Question
Calculus 1:

The sum of a number and twice another number is 10.
Find the largest possible product.

This is probably really is, but I'm terrible at calculus .. please help! thank you!

Answer
Questioner:   Courtney
Category:  Calculus
Private:  No
 
Subject:  Help!
Question:  Calculus 1:

The sum of a number and twice another number is 10.
Find the largest possible product.

This is probably really is, but I'm terrible at calculus .. please help! thank you!
 
..................................................
Hi, Courtney,

Let x = the first number.
   y = the second.
   P = the product.

Then  P = xy, to be max-ed.

and  x + 2y = 10  (the constraint)

Solve  x = 10 - 2y
Subst:  P = (10 - 2y)y

P = 10y - 2y^2

Diff:

dP/dy = 10 - 4y
Set = 0 and solve:  y = 2.5
x = 10 - 2(2.5) = 5

The numbers are 5 and 2.5 and the product is 12.5