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Published on: 13/05/2022
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Take MCQ Business Maths and Statistics Test
1.
A person wants to invest in one of three alternative investment plans: Stock, Bonds and Debentures. It is assumed that the person wishes to invest all of the funds in a plan. The pay-off matrix based on three potential economic conditions is given in the following table:
| Alternative | Economic conditions | ||
| High growth(Rs.) | Normal growth(Rs.) | Slow growth (Rs.)s | |
| Stocks | 10000 | 7000 | 3000 |
| Bonds | 8000 | 6000 | 1000 |
| Debentures | 6000 | 6000 | 6000 |
Determine the best investment plan using each of following criteria i) Maxmin ii) Minimax.
2.
The following table summarizes the supply, demand and cost information for four factors S1, S2, S3, S4. shipping goods to three warehouses D1, D2, D3.
Find an initial solution by using north west corner rule. What is the total cost for this solution?
3.
4.
A farmer wants to decide which of the three crops he should plant on his 100-acre farm. The profit from each is dependent on the rainfall during the growing season. The farmer has categorized the amount of rainfall as high medium and low. His estimated profit for each is shown in the table.
| Rainfall | Estimated Conditional Profit(Rs.) | ||
| crop A | crop B | crop C | |
| High | 8000 | 3500 | 5000 |
| Medium | 4500 | 4500 | 5000 |
| Low | 2000 | 5000 | 4000 |
If the farmer wishes to plant only crop, decide which should be his best crop using
(i) Maximin
(ii) Minimax
5.
Given the following pay-off matrix(in rupees) for three strategies and two states of nature.
| Strategy | States-of-nature | |
| E1 | E2 | |
| S1 | 40 | 60 |
| S2 | 10 | -20 |
| S3 | -40 | 150 |
Select a strategy using each of the following rule
(i) Maximin
(ii) Minimax
1.
| Economic Conditions | |||||
| Alternative | High growth | Normal growth | Slow growth | Minimum payoff | Maximum payoff |
| Stocks | 10000 | 7000 | 3000 | 3000 | 10000 |
| Bonds | 8000 | 6000 | 1000 | 1000 | 8000 |
| Debentures | 6000 | 6000 | 6000 | 6000 | 6000 |
(i) Max (3000, 1000, 6000) = 6000
∴ Debentures is the best using maximin principle
(ii) Max (10000, 8000, 6000) = 6000
∴ Debentures is the best using minimax principle.
2.
West Corner Method :
Here total supply = 5 + 8 + 7 + 14 = 34
total demand = 7 + 9 + 18 = 34
total supply = total demand
∴ The given problem is a balanced transportation problem.
Hence, there exists a feasible solution to the given problem.
I - allocation:
[∵ min (5, 7) = 5]
II - allocation:
[∵ min (2, 8) = 2]
III - allocation:
[∵ min (9, 6) = 6]
IV - allocation:
[∵ min (3, 7) = 3]
V - allocation:
[∵ min (18, 4) = 4]
VI - allocation:
[∵ min (14, 14) = 14]
Thus, the allocation are
∴ The transportation schedule is
S1 → D1, S2 → D1, S2 → D2, S3 → D2, S3 → D3, S4 → D4
Hence total transportation cost
= 5 (2) + 2 (3) + 6 (3) + 3 (4) + 4 (7) + 14 (2)
= 10 + 6 + 18 + 12 + 28 + 28 = Rs. 102
3.
4.
| Estimated Conditional Profit 0 | |||||
| Rainfall | High | Medium | Low | Minimum payoff | Maximum payoff |
| Crop A | 8000 | 4500 | 2000 | 2000 | 8000 |
| Crop B | 3500 | 4500 | 5000 | 3500 | 5000 |
| Crop C | 5000 | 5000 | 4000 | 4000 | 5000 |
(i) Max (2000,3500,4000) = 4000
∴ Crop C is the best according to maximin criteria
(ii) Min (8000,5000,5000) = 5000
∴ Crop B and C are best according to minimax criteria
5.
| Strategy | States-of-nature | Minimum payoff | Maximum payoff | |
| E1 | E2 | |||
| S1 | 40 | 60 | 40 | 60 |
| S2 | 10 | -20 | -20 | 10 |
| S3 | -40 | 150 | -40 | 150 |
(i) Max (40,-20,-40) = 40
∴ Strategy S1 is the best accordirtg to maximum criteria
(ii) Min (60,10,150) = 10
∴ Strategy S2 is the best accordirtg to minimax principle.
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Tamilnadu Stateboard 12th Standard Subjects
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