Question 143366
You are looking for total revenue, R, as a function of price.  Total revenue is the number of items sold times the price of each.  It just so happens in this case that the number of items sold, N, is itself a function of the price.


N(p) is given:  {{{N(p)=2000-100p}}} and we have defined R(p) as {{{ R(p)=p*N(p)}}}, or {{{R(p)=p(2000-100p)=2000p-100p^2}}}


Notice that at $20, the number of shirts sold, according to the given quantity sold model, is zero, hence the revenue will also be zero.  It would seem that {{{N(p)=2000-100p}}} is a rather poor real-world model for the relationship between price and number sold for rugby shirts which typically range in the $30 to $50 range, though I have seen some fetching $120 and up.