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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 = 66 and P = x y is maximized a. Solve x + y = 66 for y. y = 0 b. Substitute the result from part a into the equation P = x 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, Type your answer in interval notation.) dp d. Find -. Solve the equation dy = 0. dP dx = Solve the equation. x =(Use a comma to separate answers as needed.) 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) = (Simplify your answer.) Determine P(44). P(44) = (Simplify your answer.) Find P(66). P(66) = (Simplify your answer.) f. Give the maximum value of P, as well as the two numbers x and y for which x y is that value. The maximum value of P is The values of x and y are x = ]and y =]