00:03
About question number 17, we have, we are given a profit function of a product company where a is the amount spent on advertisement and p is the price charged for item.
00:13
We need to find the maximum profit.
00:16
So to maximize this, first we'll find p .a that is differentiating with respect to a, keeping p as a constant.
00:22
So we get 2p minus 2a p over 10.
00:29
We find p, that is differentiating.
00:31
With respect to p which is price so we have 2a plus 80 minus 30p minus a square over 10 we find p a a which is just negative 2 p over 10 we find p a p a which is just negative 2p over 10 we find p a p which is just negative 2 over 10 and we find p with double differentiating with respect to price so we have negative 30 only because everything else is with respect to a which will just become zero.
01:11
All right so now we got to solve pa equal to zero and pp equal to zero in order to get the critical points so if we set, excuse a different color here so if we set ppa as zero it means that if we take two p out we are left with one minus a over 10 so that is equal to zero so from here we get two solutions one p is 0 and another one is 1 minus a over 10 is 0 it means that a is 10 and now we'll substitute those values over here to get the to get the value the corresponding values of the other terms so if a is 10 let's write p b first so that is 2a plus that is 2a plus 80 minus 30p minus square or 10...