Star Brite Media (SBM), an independent video rental store, carries digital projection systems that customers can rent out together with new, high-definition DVDs. The store manager is forecasting that, in an average week, about 21 customers would ask to rent a projection system, the exact number of requests per week being random and may be assumed to be Poisson distributed. Their projection rental time is estimated to follow exponential distribution with a mean of about 3 days. (SBM is open 7 days per week.)
a. What is the minimum number of projection systems Sandra should buy to ensure a service level of 90%, i.e., that the probability that a projection system is available when a customer requests to rent one is about 90%? (Assume that customers who are interested in renting a projection system but do not find one available do not wait, but go to find one at another store.)
b. Instead of buying outright, SBM has the option of leasing the projection systems at a special rate of $199 per month per projection system. (This includes insurance on the systems.) What is the break-even price that SBM should charge per day for renting out a projection system? (Assume 30 days per month, an average rental length of 3 days, and a service level of 90%.)

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The Answer of Star Brite Media (SBM), an independent video rental store, carries digital projection systems that customers can rent out together with new, high-definition DVDs. The store manager is forecasting that, in an average week, about 21 customers would ask to rent a projection system, the exact number of requests per week being random and may be assumed to be Poisson distributed. Their projection rental time is estimated to follow exponential distribution with a mean of about 3 days. (SBM is open 7 days per week.)
a. What is the minimum number of projection systems Sandra should buy to ensure a service level of 90%, i.e., that the probability that a projection system is available when a customer requests to rent one is about 90%? (Assume that customers who are interested in renting a projection system but do not find one available do not wait, but go to find one at another store.)
b. Instead of buying outright, SBM has the option of leasing the projection systems at a special rate of $199 per month per projection system. (This includes insurance on the systems.) What is the break-even price that SBM should charge per day for renting out a projection system? (Assume 30 days per month, an average rental length of 3 days, and a service level of 90%.)

Star Brite Media (SBM), an Independent Video Rental Store, Carries