Question

Question 1 The director of social services of a county has learned that the state has mandated additional information requirements. This will place and additional burden on the agency. The director has identified three acceptable alternatives to handle the increased workload. One alternative is to reassign present staff members, the second is to hire and train two new workers, and the third is to redesign current practice so that workers can readily collect the information with little additional etfort. An unknown factor is the caseload for the coming year when the new data will be collected on a trial basis. The estimated costs for various options and caseloads are shown in the following table. Reassign Staff New staff Redesign collection Caseloads Moderate High $ 50 000 $ 60 000 $ 40 000 $75 000 $ 60 000 $ 60 000 Very High $ 85 000 $ 65 000 $ 90 000 Assuming that past experience has shown the probabilities of various caseloads to be unreliable, what decision would be appropriate using each of the following criteria? a. Maximin b. Maximax c. Laplace d. Minimax regret

Answer 1

Gtven dat a' a) Marimin Cnitenton mazmizcs the minimum poyott CBest of wo ut) Moderate wonst Нgh Veryhigh (minfmum) Reassign Staff 50000 60000 8S000 50000 New staff 40000 40000 6000 7S000 Peckrign 6 000 0 90000 G0000 GO0DD Collechion chevse alter native ofth the highest minimum payott H00000 New statt) Dec'ston choose COUYAL of achon Vew staft

b) Maximar Critenfon Marm?2es he ma zimum pay otf CBest of Best) Madenate High Veny high Best maxi'mum R.S 60000 SO000 6C000 75000 40000 75 000 N:S 90000 90000 R.C GO000 60000 Chooke aternative oiTh he highett maxinum Payoff 9000o CR.c) Decision choohe courAe of action Redesign Colection

Lapla ce cnttenfen- 1 Calaulate auerage payott for each altein ative Modenate Wigh Very high Aveage R.S 5O000 60000 t85000 65000 NoS 4D 000 CS000 6000 0 R.C 60000 60000 q0000 7000 0 choose altexnahive oitt hig hat averay 70000 CRederign collectiOn .: Decision choone Redesign collectio

f Mrima Rearet Cnitenion Minfmfres the maximum ne Pagrt eest payoff Payoff Received Modenatel Veryhigh igh 50000 R.S 60000 000 60000S0000 9DO0 0-SSDOD 7T000-60oDO loo00 qoo0(500 IS0O0 4o000 75000 NS 60000- 40 000 o00-75OD 90000-6SDOO 20000 =30000 60000 9o000 6000 0 R. C 60000-6000 0 70000-60000 90000-900o 15000 Regret totle Very high Moderate high Maximum Igooo R.S IS000 o000 25000 95000 20000 N.S I50 00 15000 R.c maximum Take mialmom of I5000 etthen choone Reauign staft or So decision es Redeuign collectfon

SOLUTION FOR QUESTION 2:-

a) T9 eau , MTBF 6 years PC satellite do not fail) MTBF = e (e) .5 Z O223l (above) . It fs toY move than 97ears 1- 0.2231 than 9 years tor No more 0.7769

SOlUTION FOR QUESTION 2(B):-

Caleolate the probability that the hat ell ite otll than 12 yea, have an exp ected life of more Usin1 following Pemola - Tr) PC Satellite do not fail) e MTBF

9hen e T-lengh of Senvice before failure = 12 yearn b) MTBF Mean tme before failre 6 year MTBF P CSatellfte do not fail) e - ) e = e2 -0:1353. .O.1353 s the probability that the Sat ellite wtl fnction tor more than 12 year

c) lew than 2 Years MTBF 6 years T 21 1e P( Satellite do not fail) - Ie I-O.C302 = Oc.9698 rs the proloability that the satellife - 0.9698 Less Ihan 21 year witl finction for MAre