A company has produced a new battery with an estimated mean lifetime of 60 hours. Management also believes that the standard deviation is 4.5 hours and that battery hours are normally distributed. To promote the new battery, management has offered to refund some money if the battery fails to reach 50 hours before the battery needs to be recharged. Specifically, for batteries with a lifetime below 50 hours, the management will refund a customer $50 per hour short of 50 hours.
a. For each battery sold, what is the expected cost of the promotion?b. What hours should the company set the promotion claim if it wants the expected cost to be $0.50?
What will be an ideal response?
b. The solution is obtained using a simulation optimization model with an objective of setting the expected value of cost (in cell B12) to $0.50 and setting cell B4 to be the decision variable. The solution obtained will vary slightly across optimization runs, but when rounded, a promotion claim of 49 hours will result in an average/expected cost of $0.50.
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