A model for advertising response is given by:where P (a) is the profit expressed as a function of the amount

P(a)=200-2a+10 ln a


optimal amount of advertising, a =


maximum profit, P =

A model for advertising response is given by:where P (a) is the profit expressed as a function of the amount
P(a) = 200 -2a + 10ln(a)





maximum profit is when dP/da = 0





dP/da = -2 + 10/a





so -2 + 10/a = 0





10/a = 2





2a = 10





a = 5





calculate P when a = 5





P(5) = 200 - 2(5) + 10ln(5)





=%26gt;200-10 + 10(1.609)





P(a) = 206.09





so optimal amount of advertising a = 5 and





Maximum profit, P = 206