A​ one-product company finds that its​ profit, P, in millions of​ dollars, is given by the following equation where a is the amount spent on​ advertising, in millions of​ dollars, and p is the price charged per item of the​ product, in dollars. ​P(a, p)=4ap+120p−20p2− 1 10a2p−120 Find the maximum value of P and the values of a and p at which it is attained.