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
2. Determine cumulative probabilities:
| Profit | Probability | Cumulative Probability |
|--------|-------------|------------------------|
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(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 :
| कच्चा माल | उत्पाद की प्रति इकाई आवश्यकता | ||
|---|---|---|---|
| A | B | C | |
| I | 3 | 4 | 5 |
| II | 5 | 3 | 5 |
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?
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.
Solve the following cost minimizing assignment problem.
In the inventory model with finite replenishment rate, if the replenishment rate is equal to consumption rate, the holding cost is 0.
The optimal solution of any integer linear programming problem can be obtained by rounding off the optimal solution of its LP relaxation.
An oil engine manufacture purchase lubricants at the rate of 
50 per unit from a vendor. The requirement of these lubricants is 1800 units per year. The cost of placing an order is 40 and inventory carrying cost per rupee per year is only 20 paise. Find the Economic Order Quantity (EOQ). Also find the cycle time.