A one-product company finds that its profit, ( mathrm{P} ), in millions of dollars, is given by the following equation where ( mathrm{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)=2 a p+80 p-15 p^{2}- frac{1}{10} a^{2} p-90 ] Find the maximum solutionspile.com

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A one-product company finds that its profit,  (  mathrm{P}  ), in millions of dollars, is given by the following equation where  (  mathrm{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)=2 a p+80 p-15 p^{2}- frac{1}{10} 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  (  mathrm{P}  ) is attained when a is  (  mathrm{S}  quad  ) million and  (  mathrm{p}  ) is  (  $  ) solutionspile.com

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