# Question

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?

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?

## Answer to relevant Questions

Given that a production process may experience both random and assignable variation, for which type of variation is the source generally easier to identify and eliminate? Why? “JIT manufacturing is just a gimmick for reducing inventory costs; it has nothing to do with quality.” Discuss the preceding statement. In a 3-sigma mean control chart for a process that is in control, what is the probability that a given sample mean will fall outside the control limits as the result of random variation alone? When a given process is operating properly, the percentage of defectives is 4%. What will be the 3-sigma upper and lower control limits for a p-chart in which each sample consists of 150 items? Using the control limits determined in Exercise 20.52, evaluate whether the process was in control when the following data were collected for vehicles 21–30.Post your question

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