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A​ one-product company finds that its​ profit, P, in millions of​ dollars, is given by the...

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)=4 ap + 50 p - 9 p^2 - one tenth a^2 p - 90

Find the maximum value of P and the values of a and p at which it is attained. The maximum value of P is attained when a is ​$ -------- million and p is ​$ -------?. The maximum value of P is ​$ ------- million.?

Math   Calculus   
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