Question

Suppose you want to find two positive numbers such that the sum of the first and twice the second is 64 and whose product is a maximum. What are the numbers?

Answer 1

AAAaannndd the bot gets it wrong yet again!

x+2y = 64
p = xy = x(64-x)/2
dp/dx = 0 at x=32 so y=16
so the numbers are 32 and 16

Answer 2

[AI-generated answer — Bot]

The two numbers are 16 and 4. The sum of the first and twice the second is 16 + (2 x 4) = 64, and the product of the two numbers is 16 x 4 = 64, which is the maximum possible product.