# Numericals on EMV Criterion and EOL Criterion

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

(i)Â Â Â Â Â  Using EMV criterion Â Â Â Â Â Â Â Â Â Â Â Â Â  (ii)Â Â Â Â Â Â Â  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 = `Â 1950, using EOL = `Â 1575)

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

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

(ii) Â Â Â  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.Â Â Â

 (i) Act A1 A2 A3 A4 Â (ii) Act A1 A2 A3 A4 EMV 225 161 195 420 EMV 345 400 375 151.6

3.Â Â Â Â Â Â Â Â  Given following pay â€“ 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 Â 100 S3 150 150 100 100 S4 200 100 150 200

Ans.Â Â Â

 (i) Act A1 A2 A3 A4 Â (ii) Act A1 A2 A3 A4 EMV 175 150 120 95 EOL 50 75 105 130

4.Â Â Â Â Â Â Â Â  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 `Â 50 per item other wise loss of `Â 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

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5.Â Â Â Â Â Â Â Â  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)

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6.Â Â Â Â Â Â Â Â  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

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

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#### MT UVA BMS

MT UVA- University, Vocational and Affiliated Education for BMS

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