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 plus y equals 81 and pequalsx squared y is maximized a. solve x plus y equals 81 for y. yequals 81 minus x b. substitute the result from part a into the equation pequalsx squared y for the variable that is to be maximized. pequals x squared left parenthesis 81 minus x right parenthesis c. find the domain of the function p found in part b. left bracket 0 comma 81 right bracket (simplify your answer. type your answer in interval notation.) d. find startfraction dp over dx endfraction . solve the equation startfraction dp over dx endfraction equals0. startfraction dp over dx endfraction equals nothing