Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P.

x+y=96 and P=x²y is maximized

a. Solve x+y=96 for y.

y=

b. Substitute the result from part a into the equation P=x²y for the variable that is to be maximized.

P=

c. Find the domain of the function P found in part b.

= ? (Simplify your answer. Answer in intervalnotation.)

d. Find dP/dx. Solve the equation dP/dx=0.

dP/dx=

Solve the equation

x=? (Use a comma to separate answers asneeded.)

e. Evaluate P at any solutions found in partd, as well as the endpoints of the domain found in part c.

FindP(0).

P(0)=? (Simplify youranswer.)

Determine P(64)=? (Simplify youranswer.)

Find P(96)=? (Simplify youranswer.)

f. Give the maximum value ofP, as well as the two numbers x and y for which x²y is that value.

The maximum value of P is =?

The values of x and y are x= and y=