Question 465289
Assuming all the economic demand is met and q items are sold, the amount of revenue will be pq, or


*[tex \LARGE q(\frac{80-q}{4}) = -\frac{q^2}{4} + 20q]


This is a quadratic opening downward, so the maximum revenue occurs at the "vertex" or at q = -20/(-1/2) = 40 (also halfway between 0 and 80). The revenue will be


*[tex \LARGE -\frac{40^2}{4} + 20(40) = 400]