1.         Given the following conditional cost matrix corresponding to 3 Acts  A1, A2 and A3 and 3 states of nature find best action to minimize cost :

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(i)      Using EMV criterion               (ii)        Using EOL criterion.

State of Nature

Conditional Cost in (`)

Probability

A1

A2

A3

S1

0

1,500

3,000

0.80

S2

9,000

1,500

3,000

0.15

S3

18,000

10,500

3,000

0.05

Total

1.0

(Ans. : Minimum Cost using EMV = ` 1950, using EOL = ` 1575)

 

2.         Given the following pay off matrix with probabilities of states of nature.

(i)      Find expected pay – off of each action.

(ii)     Find expected opportunity loss of each Act.

State of Nature

Course of Action

Probability

A1

A2

A3

A4

S1

100

800

– 100

0

0.15

S2

600

0

400

600

0.45

S3

– 300

200

0

600

0.25

S4

100

0

200

0

0.15

Ans.   

(i)

Act

A1

A2

A3

A4

  (ii)

Act

A1

A2

A3

A4

  EMV 225 161 195 420    

EMV

345 400 375 151.6

 

3.         Given following pay – off table find EMV and EOL of each actions. If Probabilities of occurrence of S1, S2, S3, S4 are 0.1, 0.3 and 0.4 respectively.

State of Nature

Course of Action

A1

A2

A3

A4

S1

100

50

400

50

S2

200

300

– 50

 100

S3

150

150

100

100

S4

200

100

150

200

Ans.   

(i)

Act

A1

A2

A3

A4

  (ii) Act

A1

A2

A3

A4

  EMV 175 150 120 95     EOL 50 75 105

130

4.         The demand for a seasonal item on any given day are given below :

Demand (In Units)

4

5

6

7

Probability

0.1

0.4

0.2

0.3

The items are perishable it they are sold on same day it gives. Profit of ` 50 per item other wise loss of ` 20 per item. Find pay off matrix. Use probability distribution of demand to find EMV of each act.

Ans.

Act (No. of units in store )

4

5

6

7

EMV

200

243

258

259

 

5.         A news paper distributor assigns probabilities to the demand for a magazine as follows :

Copies Demanded

10

20

30

40

Probability

0.4

0.3

0.2

0.1

A copy of the magazine sells for ` 14/- and costs ` 12. What can be maximum possible EMV if the distributor can return unsold copies for ` 10 each.

(Ans. Keep 20 copies)

 

6.         A vegetable vendor purchases fruits every morning at ` 50 a box and sells for ` 80 box. Any box remaining unsold at the end of the day can be disposed at next day at salvage value of ` 20 per box. Using past sales the vendor has following frequency distribution.

Act (No. of units in store)

4

5

6

7

EMV

200

243

258

259

            How many boxes the vendor should purchase to maximize EMV? (Ans. : 17 boxes)

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