Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 180 shirts in a week at $\$7$ per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 480 per week at $\$2$ per shirt.
Based on this information, construct a linear demand equation for Yoda vs. Alien T-shirts, and hence obtain the weekly revenue R as a function of the unit price x.
R(x) =
Best Answer
Let be $p$ the price and $q$ the quantity. We know that
So the demand function $q=a-bp$ must satisfy $180=a-7b$ and $480=a-2b$ and then $a=600$ and $b=60$. Thus the demand function is $$ q=600-60p $$ The revenue function is found multipying price by quantity: $$ R(p)=p\times q=p\times (600-60p)=600p-60p^2 $$