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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