The sum of a number and 3 times another number is 12. Their product is a maximum. Find the numbers and the max product.

Question

The sum of a number and 3 times another number is 12. Their product is a maximum. Find the numbers and the max product.

Lesson: Optimization

Answer 1

x+3y=12

y=(1/3)(12-x)

xy=(1/3)(12x-x²)

At the maximum the derivative of the product = 0, i.e. (1/3)(12-2x)=0 and x=6

Then y=2 and the maximum product is 12.