suppose the demand for a certain brand of product is give by D(p)= (-p^2)/(252)+400, where p is price in dollars...

Question

suppose the demand for a certain brand of product is give by D(p)= (-p^2)/(252)+400, where p is price in dollars... If the price, in terms of cost c, is expressed as p(c) =3c-24, find the demand function in terms of cost

Answer 1

Hi! You have the demand function in terms of price. To find it in terms of cost [in math terms, D(c)], you insert the price as a function of cost into D(p). Here goes: D(p) = (-p^2)/252 + 400 D(c) = (-(3c - 24)^2)/252 + 400 = (-(9c^2 - 144c + 576))/252 + 400 It's just down to simplifying after this. You can divide 9 out of all four numbers in the quotient, for example, and distribute the leading (-1) into the top three terms: D(c) = (-c^2 + 16c - 64)/28 + 400