JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech IV MINE SYSTEMS ENGINEERING Previous Question Paper (February/March - 2022 - R18)
Answer any five questions
All questions carry equal marks
Main
How are models classified according to purpose for which they are needed to be developed.
Answer
Models are classified based on their purpose into the following categories:
- Descriptive Models: These models describe the existing state or behavior of a system without suggesting changes. They are used to understand how a system functions under current conditions.
- Predictive Models: These are designed to forecast future outcomes or system performance based on historical data and identified trends. They help in anticipating potential issues or requirements.
- Prescriptive (Normative) Models: These models provide recommendations or optimal solutions to decision-making problems. They identify the best course of action to achieve a specific objective, such as maximizing profit or minimizing cost.
- Simulation Models: These replicate the dynamic behavior of a system over time. They are used to test "what-if" scenarios and observe the impact of changes in variables without disturbing the actual system.
- Optimization Models: A subset of prescriptive models, these are specifically formulated to find the best possible values for decision variables within defined constraints to maximize or minimize an objective function.
Solve the following LPP problem graphically:
Subject to:
Answer
To solve the LPP graphically, we identify the feasible region defined by the constraints:
- Constraint 1: 3x1 + x2 = 66. Intercepts are (22, 0) and (0, 66).
- Constraint 2: x1 + x2 = 45. Intercepts are (45, 0) and (0, 45).
- Constraint 3: x1 = 20.
- Constraint 4: x2 = 40.
The corner points of the feasible region are found by intersection:
- (0, 0)
- (20, 0)
- (20, 6) [Intersection of x1=20 and 3x1+x2=66]
- (10.5, 34.5) [Intersection of 3x1+x2=66 and x1+x2=45]
- (5, 40) [Intersection of x1+x2=45 and x2=40]
- (0, 40)
Evaluating Z = 8000x1 + 7000x2 at these points:
| Corner Point | Z = 8000x1 + 7000x2 |
|---|---|
| (0, 0) | 0 |
| (20, 0) | 160,000 |
| (20, 6) | 202,000 |
| (10.5, 34.5) | 325,500 |
| (5, 40) | 320,000 |
| (0, 40) | 280,000 |
The maximum value of Z is 325,500 at x1 = 10.5 and x2 = 34.5.
Solve the following LPP by Big M method
Subject to:
x1 + 4x3 ≤ 6
x2 - x3 = 2
x1, x2, x3 ≥ 0
Answer
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Solve the following transportation problem by finding initial basic feasible solution by Vogels method.
| Factory | W | X | Y | Z | Availability |
|---|---|---|---|---|---|
| A | 19 | 30 | 50 | 10 | 7 |
| B | 70 | 30 | 40 | 60 | 9 |
| C | 40 | 8 | 70 | 20 | 18 |
| Requirement | 5 | 8 | 7 | 14 | - |
Answer
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State the traveling salesman problem.
Answer
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Give the following across city distance table, find the minimum distance root provided his home town is in A
| From/To | A | B | C | D | E |
|---|---|---|---|---|---|
| A | ∞ | 7 | 6 | 8 | 4 |
| B | 7 | ∞ | 8 | 5 | 3 |
| C | 6 | 8 | ∞ | 9 | 7 |
| D | 8 | 5 | 9 | ∞ | 8 |
| E | 4 | 6 | 7 | 8 | ∞ |
Answer
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Two jobs are to be processed on four machines A, B, C and D. The technological order for these jobs on machines is as follows:
Job 1: A-B-C-D
Job 2: D-B-A-C
Processing times are given in the following table:
| Job | A | B | C | D |
|---|---|---|---|---|
| 1 | 4 | 6 | 7 | 3 |
| 2 | 4 | 7 | 5 | 8 |
Solve it by graphical method.
Answer
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The following failure rates have been observed for a certain type of light bulbs:
| End of week | Probability of failure to date |
|---|---|
| 1 | 0.05 |
| 2 | 0.13 |
| 3 | 0.25 |
| 4 | 0.43 |
| 5 | 0.68 |
| 6 | 0.88 |
| 7 | 0.96 |
| 8 | 1.00 |
The cost of replacing an individual failed bulb is Rs. 1.25. The decision is made to replace all bulbs simultaneously at fixed intervals and also to replace individual bulbs as they fall in service. If the cost of group replacement is 30 paise per bulb, what is the best interval between group replacement? At what group replacement price per bulb would a policy of strictly individual replacement become preferable to the adopted policy?
Answer
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Solve the following game graphically where pay off matrix for player A has been prepared.
2 4 9 -3 1
Answer
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If a product is to be manufactured within the company, the details are as follows:
Annual demand rate (r) = 36000 units, Production rate (k) = 72000 units, Setup cost (C0) = Rs. 250 per setup, Carrying cost (Cc) = Rs. 25/unit/year.
Find the i) EOQ and ii) Cycle time.
Answer
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In a bank, cheques are cashed at a single “teller” counter. Customers arrive at the counter in a Poisson manner at an average rate of 30 customers/hr. The teller takes on an average 1.5 minutes to cash a cheque. The service time has been shown to be exponentially distributed.
i) Calculate the percentage of time the teller is busy
ii) Calculate the average time a customer is expected to wait.
Answer
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Compare PERT and CPM.
Answer
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