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 :
(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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