एक परियोजना अनुसूचि के निम्नलिखित लक्षण हैं :
| गतिविधि | समय |
|---|---|
| 1 – 2 | 4 |
| 1 – 3 | 1 |
| 2 – 4 | 1 |
| 3 – 4 | 1 |
| 3 – 5 | 6 |
| 4 – 9 | 5 |
| 5 – 6 | 4 |
| 5 – 7 | 8 |
| 6 – 8 | 1 |
| 7 – 8 | 2 |
| 8 – 10 | 5 |
| 9 – 10 | 7 |
i) PERT नेटवर्क निर्मित कीजिए।
ii) क्रांतिक पथ ज्ञात कीजिए।
परियोजना अनुसूचि के लिए पहले हम PERT नेटवर्क तैयार करेंगे और फिर क्रांतिक पथ (Critical Path) का निर्धारण करेंगे। i) PERT नेटवर्क निर्माण: सभी गतिविधियों और उनके समय को ध्यान में रखते हुए हम नेटवर्क इस प्रकार बनाएंगे: * प्रारंभ बिंदु: 1 * गतिविधियाँ: | गतिविधि | समय | पूर्ववर्ती | उत्तरवर्ती | | ------- | --- | ---------- | ---------- | | 1–2 | 4 | 1 | 2 | | 1–3 | 1 | 1 | 3 | | 2–4 | 1 ______ ______ ________ ___ _____ ________ _______ _______ __________ _________ __________ ________.
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Determine the EOQ and the optimal number of orders placed in a year.
ii) Determine the optimum production lot size and the average duration of the production run.
In a factory, there are six jobs to perform each of which should go through two machines A and B in the order A B. The processing timings (in hours) for the jobs are given here. You are required to determine the sequence for performing the jobs that would minimize the total elapsed time T, what is the value of T?
| Job | Machine A | Machine B |
| J₁ | 1 | 5 |
| J₂ | 3 | 6 |
| J₃ | 8 | 3 |
| J₄ | 5 | 2 |
| J₅ | 6 | 2 |
| J₆ | 3 | 10 |
निम्नलिखित LPP की द्वैती लिखिए: का न्यूनतमीकरण कीजिए
जबकि : और x3 अप्रतिबंधित है।
निम्नलिखित LPP को ग्राफीय विधि से हल कीजिए : का अधिकतमीकरण कीजिए जबकि :
तथा ।
Which of the following statements are true? Give reasons for your answers.
i) If an item is ordered frequently, then the risk of running out of stock is least.
ii) In deterministic queuing model, arrival rate must not exceed the service rate.
iii) The critical path of a project network represents the minimum time needed to complete the project.
iv) A necessary and sufficient condition for a basic feasible solution for a minimization LPP to be optimum is that all .
v) If dual has an unbounded solution, primal has a feasible solution.
Find the optimum solution to the following transportation problem:
A firm produces there product A, B and C. It uses two types of raw materials I and II of which 5000 and 7500 units respectively are available. The raw material requirements per unit of the products are given below:
| Raw Material | Requirement per unit of product | ||
| A | B | C | |
| I | 3 | 4 | 5 |
| II | 5 | 3 | 5 |