A small project is composed of 8 activities where time estimates are listed in the table below:
| Activity | Estimated duration (in days) | ||
| Optimistic | Most likely | Pessimistic | |
| A (1, 2) | 28 | 32 | 36 |
| B (1,3) | 22 | 28 | 32 |
| C (2, 6) | 26 | 36 | 46 |
| D (3, 4) | 14 | 16 | 18 |
| E (3, 5) | 32 | 32 | 32 |
| F (3, 6) | 40 | 52 | 74 |
| G (4, 5) | 12 | 16 | 24 |
| H (5, 6) | 16 | 20 | 26 |
Draw the project network diagram. Using the PERT find the expected time and variance for each activity.
To draw the project network diagram and find the expected time and variance for each activity using PERT (Program Evaluation and Review Technique), we need to follow these steps:
- Draw the project network diagram:
The activities and their precedence relationships are represented in the following network diagram:
A
/ \
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) 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।
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) 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.
For a Queuing Model (M/M/1): (GD/∞/∞) with one server, if the service rate µ increases, the expected number of customers in the system decreases.
दिया गया है कि इकाइयाँ,
इकाइयाँ,
इकाइयाँ,
इकाइयाँ,
इकाइयाँ और
इकाइयाँ हैं। क्या यह निम्नलिखित परिवहन समस्या का इष्टतम हल है ?
उपलब्ध इकाइयाँ
आवश्यक इकाइयाँ
यदि यह इष्टतम हल नहीं है, तो इसे प्रयोग करके एक बेहतर सुसंगत हल निकालिए।
A sugar manufacture has two production processes. In one hour, Process I makes 100 kg of Grade I (high quality) sugar and also produces 140 kg of Grade II sugar as a byproduct. Process II makes in one hour 60 kg of Grade I (high quality) sugar and also produces as a by-product 40 kg of Grade II sugar. The manufacture is confident that during the festival season all the sugar that is made can be sold. He has committed to selling at least 6000 kg of Grade I and 5600 kg of Grade II for the season. The revenue earned by selling one kilogram of Grade I sugar is ₹ 4 (irrespective of the process used) and the revenue earned by selling one kilogram of Grade II sugar is ₹ 2 (irrespective of the process used). Formulate the problem of maximizing the total revenue earned as an LPP. Solve the problem by graphical-method.
In an optimal solution of the LPP
s.t.
both cannot be positive.
A small project is composed of 8 activities where time estimates are listed in the table below:
| Activity | Estimated duration (in days) | ||
| Optimistic | Most likely | Pessimistic | |
| A (1, 2) | 28 | 32 | 36 |
| B (1,3) | 22 | 28 | 32 |
| C (2, 6) | 26 | 36 | 46 |
| D (3, 4) | 14 | 16 | 18 |
| E (3, 5) | 32 | 32 | 32 |
| F (3, 6) | 40 | 52 | 74 |
| G (4, 5) | 12 | 16 | 24 |
| H (5, 6) | 16 | 20 | 26 |