An assignment problem can be considered as a special case of transportation problem.
In operational research, the assignment problem is indeed closely related to the transportation problem, but it is not merely a special case; rather, it represents a specific application within the broader framework of optimization.
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निम्नलिखित में से कौन-से कथन सत्य हैं और कौन-से असत्य हैं ? अपने उत्तर के पक्ष में एक संक्षिप्त उपपत्ति या प्रति-उदाहरण दीजिए :
(i) यदि एक उत्पाद बार-बार ऑर्डर किया जाता है, तो स्टॉक की पुनरावृत्ति लागत का जोखिम कम होता है।
(ii) एक पंक्ति निर्देश के हल के लिए, आगमन दर, सेवा दर से अधिक नहीं होनी चाहिए।
(iii) एक परियोजना नेटवर्क का क्रांतिक पथ उस परियोजना को पूरा करने में लगने न्यूनतम काल को दर्शाता है।
(iv) एक अधिकतमकरण LPP के आधार सुसंगत हल के लिए आवश्यक और अनिवार्य प्रतिबंध है कि सभी `Z_j - C_j >= 0`
(v) यदि द्वैती अपरिबद्ध है, तो आद्य का सुसंगत हल होता है।
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.
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?
Write the dual of the following LP problem:
Min.
Subject to
Customers come to a coffee shop at the average rate of 32 per day (8 hours a day) in Poisson pattern. The waiter employed to serve the customers has left the job. The owner of the shop wants to hire a new the job. The owner of the shop wants to hire a new waiter. Two applicants, Abdul and Raju, have applied for the post. The service times of Abdul and Raju are exponentially distributed with mean 12 minutes and 10 minutes, respectively. Abdul and Raju demand salaries of ₹ 135 and ₹ 165 per day, respectively. If no service is available, the average loss to the owner is ₹ 400 per day. Who among the two should be selected for the job?
) 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।
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