Please answer these questions.

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= 87 and P = x y is maximized a. Solve x + y = 87 for y. y= 87-X b. Substitute the result from part a into the equation P = x y for the variable that is to be maximized. P = 87x2 - x3 c. Find the domain of the function P found in part b. (Simplify your answer. Type your answer in interval notation.) d. Find dP dx Solve the equation - dP dx 7 = 0. 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(58}. % P(58] = D (Simplify your answer.) Find P(8?}. P(8?] = D (Simplify your answer.) f. Give the maximum value of Pr as well as the two numbers 2:: and y for which y is that value. The maximum value of P is D. The values of x and y are x = and y =