Based on the previous data, the probabilities of a batsman making various scores in One Day Internationals are given below:
| Runs | 10 | 20 | 30 | 50 | 60 | 70 | 100 |
| Probability | 0.01 | 0.20 | 0.15 | 0.30 | 0.12 | 0.2 | 0.02 |
Simulate the runs scored by the batsman in the next five One Day Internationals using the following 25, 39, 65, 76, 12.
To simulate the runs scored by a batsman in the next five One Day Internationals using the given probabilities, we can use a random number generator or a table of random numbers. We'll match each generated random number with the corresponding probability distribution to determine the runs scored. Here's a step-by-step simulation for the five matches _____ _________ ________ ___ ___ __________ ___.
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Find the critical path for the project whose network diagram is given below
(a) A company has three factories 1 2 F ,F and F3 which supply goods to four warehouses 1 2 3 W ,W ,W and . W4 The daily factory capacities of 1 2 F ,F and F3 are, respectively, six units, one unit and ten units. The demand of the warehouses 1 2 3 W ,W ,W and W4 are, respectively, seven, five, three and two units. Unit transportation cost are as follows:
Find an initial basic feasible solution by the Vogel’s approximation method
(b) Three custom officers check the luggage of the passengers of an airport. The passengers are found to arrive at an average rate of 30 per 8 hours a day. The amount of time a custom officer spends with the passenger is found to have an exponential distribution with mean service time 32 minutes.
(i) Find the probability that all the custom officers are idle.
(ii) Find the expected number of passengers in the queues.
(iii) Find the expected waiting time of passenger in the system
Which of the following statements are true and which are false? Give a short proof or a counter example in support of your answer.
(a) The optimal solution for the following LPP is z = 30 :
Subject to
(b) The optimal solution of an ILLP can be obtained by rounding off the optimal solution of its LP relaxation.
(c) If the availabilities and requirements of a balanced transportation problem are integers, the optimal solution to the problem will have integer values.
(d) The following max /3/4 F / F problem can be reduced to a machine problem
(e) For the mixed generator (mod 8 ) if
then 3 r is zero.
Use the simplex method to solve the following L.P.P.
Max
Subject to
The optimal solution of a maximization type LPP is given in the following table:
(i) Find the alternative optimal basic feasible solution.
(ii) Find an alternative optimal non-basic feasible solution.
Solve the ILLP given below by graphical method:
Maximum
Subject to the Constraints
are non-negative integers.
A contractor has to supply 10,000 bearings per day to an automobile manufacturer. He finds that when he starts production run, he can produce 25,000 bearings per day. The cost of holding a bearing in stock for one year is Rs. 2 and the set up cost of a production run is Rs. 180. Find the EOQ. How frequently should the production run he made