For several years, Thorndike Sports Equipment has been one of the suppliers of refreshments to the Titans of Tennis national tournament. Luke Thorndike doesn’t really like to call the company’s product a “refreshment,” since it’s been scientifically designed to replenish the fluids and vital body chemicals lost through perspiration and exercise. According to the elder Thorndike, Thornado is not “just another sugar-fluffy soft drink. It helps athletes perform at their best.”
Naturally, each competing athlete is given a complimentary carton of Thornado. However, the Thorndikes must decide how many cans of the product to send to the tournament for fan consumption. The Thorndikes make a profit of $0.25 on each can of Thornado purchased at the tournament. Each can that is not purchased is distributed to local sports clubs in the tournament’s host city. Luke Thorndike believes in helping those in need, but is quick to point out that it costs him a total of $0.80 to produce and distribute each of these unsold cans of Thornado.
Luke believes in charity, but he is also rather frugal in making it available. He’s asked Ted to figure out how many cans of Thornado to send to the Titans of Tennis tournament in order to make as much profit as possible. Ted Thorndike, having analyzed past sales patterns for Thornado at this tournament, has found annual tournament sales of the product to be closely approximated by a normal distribution with μ = 4500 cans and σ = 300 cans. In order to satisfy his grandfather’s dictate that profit be maximized, how many cans of Thornado should Ted plan on shipping to the Titans of Tennis?