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.

Question

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)=2ap+240p-25p^2-1/10a^2p-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.

Steve · Answer

Set the partial derivatives to zero for extrema. Both must be zero.

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.

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.