Mark Ting works for Sucker’s Jams and Jellies and is preparing a supermarket display to highlight the company’s many offerings. Mark’s previous exhibit was criticized by his boss, Bianca Regina who said “Jam to the left of me, jam to the right of me, but never jam in front of me!” So now Mark is under strong pressure to do well. He hired an expensive economic consultant who discovered that if x types of jam are exhibited, the probability that a given passerby will stop and look is given by max{x/20, 1}. Furthermore, if someone stops and looks, the probability that he will buy is given by max{1 − (x/20), 0}.
(a) If x types of jam are exhibited and 1, 000 people walk by, how many will stop to look on average? ___________________
(b) If x types of jam are exhibited, how many of the people who pass by will actually purchase jam? _____________
(c) In the graph below, plots sales as a function of x.
(d) If Mark chooses x to maximize sales, what value should he choose? __________
(e) How many jars of jam does he sell? _______________