Answer:
X = 8, y = 8
Step-by-step explanation:
This question is an optimization problem. Two equations are going to be needed here
n = x+y
P = xy
Such that 64 = xy
When we divide through by x we get:
y = 64/x
So that n becomes:
n = x + 64/x
n = x+64x^-1
We take derivative
n' = 1-64x^-2
When n' = 0 then a min|max occurs
0 = 1-64x^-2
Such that:
64/x² = 1
Divide through by x²
64 = x²
x = √64
x = 8
Remember y = 64/x
So,
Y = 64/8
Y = 8.
X = 8, y = 8
Thank you!
