ezto-cf-media.mheducation.com/Media/Co.. 1.00 points PA 13-11 Share&Care; is a n
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ezto-cf-media.mheducation.com/Media/Co.. 1.00 points PA 13-11 Share&Care; is a nonprofit car share company... Use Table 13.10 Share&Care; is a nonprofit car share company that rents cars. When a customer makes a reservation, they specify their pick up time and the number of time slots they will hold the vehicle, where each time slot equals 15 minutes. For example, if the pick up time is 1pm, then possible drop off times are 1:15 (1 slot), 1:30 (2 slots), etc. Share&Care; charges $2.00 for each time slot in the reservation. To discourage customers from returning the rented cars beyond their drop off time, they charge $20 per time slot used beyond the drop off time. For example, if a customer's drop off time is 2:30 and he returns the vehicle at 2:47, then he is charged $40 for the 2 time slots he used beyond his reservation (and of course, $2.00 per slot that he reserved). Larry runs a small business that makes deliveries on Fridays. To ensure availability of a car, he books his car 2 days in advance. However he doesn't know his exact needs when he books. Table 13.10 provides information regarding Larry's demand (in terms of slots). For example, if he needs 5 slots but booked 4 slots, then he uses the car for 5 slots-for a total charge of 4 x S2.00 + $20 = $28. If he ends up booking the car for more time than he needs, the extra time on the car has no value to TABLE 13.10 The Distribution Function, F(Q), and Expected Leftover In for the Number of Slots Larry Needs F(O) 0183 0916 2381 4335 6288 7851 8893 9489 9786 9919 9972 9991 9997 I(O) 0.00 0.02 0.11 0.35 0.78 1.41 2.20 3.08 4.03 5.01 6.00 7.00 8.00 9.00 10.00 0 2 3 Suppose he books the car for 1 time slots. How likely is he to pay $60 or more in d late fees? Use Table 13.10 6 7 8 9 10 (Round your answer to 4 decimal places.) To minimize his rental costs, how many time slots should Larry reserve? Use Table 13.10 and round-up rule. Suppose he books the car for 5 time slots. How many time slots can he expect to waste (i.e., they end up being of no use to him)? Use Table 13.10. Round your answer to 2 decimal places.) Lamy hates paying any late penalty fee. Suppose he wants to be 99.0% sure that 13.10 and round-up rule. d. he will not have to pay a late fee. How many slots should he book? Use Table 13 .0000Explanation / Answer
a) With 1 time slot booked, likelihood of paying $ 60 or more in late fees occur when the actual demand is of 4 slots of more.
Probability of 4 slots of more = 1 - 0.4335 = 0.5665
b) Cost of reserving 1 slot less than actual demand, Cu = 20-2 = 18
Cost of reserving 1 slot more than actual demand, Co = 2
Critical ratio = Cu/(Cu+Co) = 18/(18+2) = 0.90
Lookup F(Q) = 0.90 in table 13.10, the corresponding Q = 7
Therefore, Larry should reserve 7 slots
c) Refer table 13.10, expected left over I(Q) corresponding to Q=5 is 1.41
d) For 99% service level, corresponding value of Q = 9
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