find the optimization value of P, x+y=63 and P=x^2(y) are maximized. Nonnegative

Question

help me solve this

Answer 1

P=x²y

 

x+y=63  => y=63-x

 

P=x²(63-x)

 

P=63x²-x³

 

dP/dX = 126x-3x²

 

For maximum value of P, dP/dx = 0

 

126x-3x² = 0

 

x=0 or x=41

 

x=0 yields the local minimum for P and P(0,63) = 0

 

x=41 yields the absolute maximum for P and P(41,22)=36,982