Question
An investment company wants to study the investment proposals based on the profit factor. While analyzing a new investment proposal, the company estimated the probability distribution for the profit as follows:
| Profit (in thousands) | 3 | 5 | 7 | 9 | 10 |
| Probability | 0.1 | 0.2 | 0.4 | 0.2 | 0.1 |
Using the random numbers:
19, 7, 90, 2, 57, 28
Simulate the profit of the company for six trials.
To simulate the profit of the company for six trials using the provided probability distribution and random numbers, we can follow these steps:
1. Generate random numbers.
2. Match the random numbers with cumulative probabilities to determine the profit.
Let's proceed with the calculations:
1. Generate random numbers: 19, 7, 90, 2, 57, 28
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In an optimal solution of the LPP
s.t.
both cannot be positive.
Solve the following LPP by Simplex method:
such that
From the optimal table of the solution to the problem find the optimal solution of the dual of the problem. Verify complementary slackness property for the primal-dual pair.
Write the dual of the following LP problem:
Min.
Subject to
The time taken by a TV repair person to repair a TV set is exponentially distributed with mean 30 minutes. She repairs the sets in the order in which they come in. The arrival rate of the sets is approximately Poisson with an average rate of 10 per 8 hours day. Answer the following questions: (5)
i) What is the repair person’s expected idle time each day?
ii) How many jobs are ahead of the arriving set just brought in?
iii) What is probability that there are 2 or more sets in the system?
) The following is the optimal table of a maximising LPP where are slack variables.
Suppose a new constant 8 2x1 + x2 ≤ is added to the LPP. Find the new optimal solution of the resulting LPP.
) निम्नलिखित LPP को ग्राफीय विधि से हल कीजिए :
z = 2x₁ + 3x₂ का अधिकतमीकरण कीजिए
जबकि :
x₁ + x₂ ≤ 30
x₁ - x₂ ≥ 0
x₂ ≥ 3
0 ≤ x₁ ≤ 20
तथा 0 ≤ x₂ ≤ 12
3. (क) निम्नलिखित LPP को हल करने के लिए एकघा विधि का प्रयोग कीजिए : का अधिकतमीकरण कीजिए
जबकि : 5
तथा
(ख) निम्नलिखित LPP की द्वैती लिखिए : 5
z = 2x₁ + 3x₂ + 4x₃ का न्यूनतमीकरण कीजिए
जबकि :
2x₁ + 3x₂ + 5x₃ ≥ 2
3x₁ + x₂ + 7x₃ = 3
x₁ + 4x₂ + 6x₃ ≤ 5
x₁, x₂ ≥ 0 और x₃ अप्रतिबंधित है।
Sure, here's the text from the image:
Listed in the table below are the activities and sequencing requirements necessary for the completion of a project.
| Activity | Predecessor | Duration in weeks |
| A | __ | 6 |
| B | A | 24 |
| C | A | 6 |
| D | A | 12 |
| E | A | 9 |
| F | C,D,E | 18 |
| G | B,F | 12 |
| H | G | 24 |
i) Draw a net work diagram for the project.
ii) Find the critical path and the duration for the completion of the project.
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