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Complete parts A through F below to find nonnegative numbers x and y that satisfy the...

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=63 and P=x^2 y is maximized (For P=x^2 y, Y is not apart of the exponent, its apart of the equation, )

A. Solve for x+y=63

B. Substitute the result from part a into the equation P=x^2 y

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

D. find dP/dx. Solve the equation dP/dx=0

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).

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

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