4 of 4 4. Ken is the owner of OilCo. At the present time, Ken is forced to cousi
ID: 3206509 • Letter: 4
Question
4 of 4 4. Ken is the owner of OilCo. At the present time, Ken is forced to cousider purchasing more equipment for OilCo because of the coupetitiou. He has three alternatives: Sub100, Oiler J, and Texan. He has to select from one of the three alteraatives: Subl00, Oiler J, and Texaa. If Ken purchase a Subl00 and if there is a favorable market, he will realize a profit of S10,00. On the other hand, if the market is unfavorable, Ken will suffer a less of S170,000. If Ken purchases an Oiler Jand if there is a favorable market, he will realize a profit of $270,000. On the other hand, if the market is unfavorable, Kea will suffer a loss of 8130,000. If Ken purchases a Texan and if there is a favorable market, he will realize a profit of S80,000. On the other hand, if the market is unfavorable, Ken will suffer a lor s of $20,000. a) Develop a decision table. States of Nature Alternatives Favomalie Oiler J 270.000 -130.000 80.000 -20000 T Faworable Unfavorable Optimistic Pessimistic Sub100 310.000 -170.000 310.000 -170.000 Oiler J b) Which equipment shonald be Nelected bused on the optimistic criterion? Sub100. This equipment has the best profit SS10.000 (max 310.000, 270,000, 80,000)). e) Which equipment should be selected based on the pessimistic criterion? Texan. This equipment has the best of the min values. S-20000 (maxl-170.000, -130.000. -20.000) Favorable Unfasurabled Hurwicz (a-07 Laplace Sub100 310,000 170000 0.7 310,000 +0.3 170,000 196.000 (310,000 +-170,000)/2 20,000 Oiler J 270,000 -130,000 07-220,000 +0.3 130,000 150,000 (270,000 130,000)/2 70,000 Texan 80,000 -2,000 0.7 80,000 013 -20,000 30,000 180,000 -20,000)/2 30,000 d) Which equipment siacould be selected bused on The Hurwicz approach using a coefficient of realisan value of 0.7? Sub100. This equipment has the best prodit S166000 (max(166000, 150,000, 50.000h). e Which equipment should be selected based oa the Laplace criterion? Sub100 or Oiler J. This equipment has the best peoft $70,000.Explanation / Answer
a)
Above is the regret table and based on the above table, we would have to select Oiler J because we choose the alternative with the minimum value of the maximum amongst the two alternatives in minimax regret criterion.
b)
By multiplying Favourable states of nature with 0.6 and unfavourable with 0.4, we get the below table:-
Hence, we should select Sub100.
C)
EVPI=EVwPI-EVwoPI
We already know that EVwoPI is 118000 based on the above table. To calculate EVwPI, we have to multiply the probability with the highest amongst the favourable and unfavourable. Hence, EVwPI=(186000)(0.6)+(-8000)(0.4)=111600-3200=108400
EVPI=108400-118400=-10000
D)
a)
Above is the regret table and based on the above table, we would have to select Oiler J because we choose the alternative with the minimum value of the maximum amongst the two alternatives in minimax regret criterion.
b)
By multiplying Favourable states of nature with 0.6 and unfavourable with 0.4, we get the below table:-
States of Nature Alternatives Favourable Unfavourable Sub100 186000 -68000 118000 Oiler J 162000 -52000 110000 Texan 48000 -8000 40000Hence, we should select Sub100.
C)
EVPI=EVwPI-EVwoPI
We already know that EVwoPI is 118000 based on the above table. To calculate EVwPI, we have to multiply the probability with the highest amongst the favourable and unfavourable. Hence, EVwPI=(186000)(0.6)+(-8000)(0.4)=111600-3200=108400
EVPI=108400-118400=-10000
D)
Based on the regret table above, Texan would minimize the opportunity lossRelated Questions
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