WHAT AM I DOING WRONG?

[Maryanne]

O.k I'm pretty sure my steps are correct......... but I can't seem to get the right answer!

Question: The sum of a number and four times another number is 32. Find the numbers if their product is a maximum.

Let x represent the first integer

Let y represent the seond integer

1. X + 4Y= 32 X=32-4Y

2. XY= M


(32-4Y)(4Y)=M

128-16y^2=y

y= -16y^2+128y

= -16(x^2-8x)

= -16(x^2-8x+16-16)

= -16(x-4)^2+256

Vertex= (4, 256)

So The maximum is 256 but it doesn'y make sense for x to equal four? any help would be appreciated.

 

[galactus]

(32-4Y)(4Y)=M I believe this is the error.

Should be \(\displaystyle (32-4y)y=32y-4y^{2}\)

\(\displaystyle \frac{DM}{dy}=32-8y\)

\(\displaystyle 32-8y=0\rightarrow\\y=4\)