# Practice Questions on Decision Theory

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1.         The research department of Hindustan Lever has recommended to the marking department to launch a shampoo of three different types. The marking manager has to decide one of the types of shampoo to be launched under the following estimated pay offs for various levels of sales :

 Types of Shampoo Estimated levels of Sale (units) 15,000 10,000 5,000 Egg Shampoo 30 10 10 Clinic Shampoo 40 15 5 Deluxe Shampoo 55 20 3

What will be the marking manager’s decision if

(i)      Maximum

(ii)     Minimax

(iii)    Maximax and

(iv)    Laplace criteria are applied?

2.         The ABC Company is faced with four decision alternatives relating to investments in a capital expansion programme. Since these investments are made in future, the company foresees different market conditions as expressed in the form of states–of –nature. The following table summarizes the decision alternatives, the various states–of–nature and the rate of return associated with each state–of–nature.

 Decision States – of – nature q1 q2 q3 D1 17% 15% 8% D2 18% 16% 9% D3 21% 14% 9% D4 19% 12% 10%

If the company has no information regarding the probability of the occurrence of the occurrence of the three states–of–nature, give the recommended decision for the decision criteria listed below :

(i)      Maximax criterion

(ii)     Maximin criterion

(iii)    Minimax regret criterion

(iv)    Laplace retional criterion

3.         The ABC Company is faced with four decision alternatives relating to investment in a capital expansion programme. Since these investments are made in future, the company foresees different market conditions as expressed in the form of states–of –nature. The following table summarizes the decision alternatives, the various states – of – nature and the rate of return associated with each state – of nature.

 Decision State – of – nature q1 q2 q3 D1 17% 15% 8% D2 18% 16% 9% D3 21% 14% 9% D4 19% 12% 10%

If the company has no information regarding the probability of the occurrence of the three states – of – nature, give the recommended decision for the decision criteria listed below :

(i)      Maximax criterion

(ii)     Maximin criterion

(iii)    Minimax regret criterion

(iv)    Laplaces’s rational criterion

(v)     Hurwicz alpha criterion (a = 0.75)

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