Question

M6_A4. A restaurant's reservation agent takes reservations for dinner by telephone. If he is already on the phone when a patron calls to make a reservation, the incoming call is answered automatically, and the customer is asked to wait for the agent. As soon as the agent is free, the patron who has been on hold the longest is transferred to the agent to be served. Calls for reservations come in at a rate of about 17 per hour. The agent is able to make a reservation in an average of three minutes. The agent is paid $13 per hour. The restaurant estimates that that the restaurant loses $20 due to goodwill and dissatisfaction for every hour customers are waiting to talk to an agent a) What is the hourly system cost for the situation where the restaurant has only one agent to take calls? (Enter two decimal places) b) The restaurant is considering adding a second agent who would also be paid $13 per hour. What is the hourly system cost for the situation where the restaurant has two agents to take calls? |(Enter two decimal places) c) Should the restaurant hire the second agent?

Answer 1

LA restaurants reseruation agent takes reservations ^or dinner bt telephone. rbhe is alteady on the phone when cals to ake reservation. Aweroge stem number o customer in seruice Hmne u= 3/minuse-20h Average costProviding per seYu er our s emuice Cs 13/hour per hour waiting cost to j 20hour Ccustomer y estaurant average number ") waiting customer in queue L ku-1) 20-17 . L 5.67 our tem cost tor restaurant one Ce XL)Cs+S) (20XS.64) tC12 *I) Total cost 13. 4 13 26. the situato* d, system cost ad ded to Theretore the is 126.4 Ti the Second ogent cals then, then the to tal cosf take is coputed. agent to restayrant adding the second agemt the system On

3tem coith poisson and service times MIMIS queuin q inter- amjual times exponential S 2 arhe re s is the no. we seruers . $tem is that the The probabilitj emptd fora MM Is P。ニ K O Prs) Poニ0.40o36 number customiT in MIMIS The au s+em tor 9ueuing ystem Po S-1 (S-A)2 (0.4036)17 2 0 03メた」 2 0 C2-1 C2x20-17)2 (289) o.4o3 6) 5 29 17 +20 1.0 704 Hourl stem cost or the yestaurant ogent with two Total cost 201.0704+ C1812) - 41.40

ourlsste m cost for he situation S Yes, the restaurant should n ire the bd hiring second it is total second aa ent aaent ost issauing Phe C126.4 4.40) 79