Solve the following cost minimizing assignment problem.

 (क) एक फर्म तीन उत्पाद A, B और C बनाती है। यह दो प्रकार I एवं II का कच्चा माल प्रयोग करती है जिसकी क्रमशः 5000 और 7500 इकाइयाँ उपलब्ध हैं। प्रत्येक उत्पाद की इकाइयों के लिए आवश्यक कच्चा माल नीचे दिया गया है :

) 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 production department for a company requires 3,600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is ₹ 36 and the cost of carrying inventory is 25 percent of the investment in the inventories. The price of the raw material is  10 per kg.

 Determine the following:

i) Economic order quantity
ii) Optimal order cycle time and
iii) Minimum yearly inventory cost. 

Use the dual simplex method to solve the following L.P.P.

Subject to

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.

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?