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=60 and P = x y is maximized a. Solve x + y = 60 for y. 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.) d. Find dP dP dx -. Solve the equation dx - =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(40).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=60 and P = x y is maximized dx dx 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(40). P(40) = (Simplify your answer.) Find P(60). P(60) = (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 =