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=105 and P=x^2 y is maximized

a. Solve x+y=105 for y.

y=______

b. Substitute the result from part a into the equation P=x^2 y for the variable that is to be maximized.

P=

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

(Simplify your answer in interval notation.)

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

dP/dx=______

Solve the equation.

x=________

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

Find P(0).

P(0)=______

Determine P(70).

P(70)=______

Find P(105)

P(105)=______

f. Give the maximum value of P, as well as the two numbers x and y for which x^2 y is that value.

The maximum value of P, as well as the two numbers x and y for which x^2 y is that value.

The maximum value of P is ______

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