Download JNTUH MCA 2nd Sem R13 2019 April-May 812AK Operations Research Question Paper

FirstRanker.com

Code No: 812AK

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

--- Content provided by‌ FirstRanker.com ---

FirstRanker.com

R13

MCA 1I Semester Examinations, April/May - 2019

OPERATIONS RESEARCH

Time: 3 Hours Max. Marks: 60

--- Content provided by FirstRanker.com ---

Note: This question paper contains two parts A and B.

Part A is compulsory which carries 20 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 8 marks and may have a, b, c as sub questions.

PART - A 5 x 4 Marks =20

1. What are the shadow prices? What is its significance in simplex method of solving LPP? [4]
2. What is the difference between transportation problem and an assignment problem? [4]

--- Content provided by‍ FirstRanker.com ---

3. What are the conditions recommended for the replacement of a machine with a new one when you already have an old one? [4]
4. Distinguish between the games with saddle points and games without saddle points. [4]
5. What are the assumptions used in deriving EOQ formula? [4]

PART -B 5 x 8 Marks =40

1. Solve the following LPP using graphical method. Maximize Z=10x1 + 8x2 Subject to x1 + 2x2 < 1000 x1 < 300 x2 < 500, and x1, x2 > 0 [8] OR A company wants to purchase at most 180 units of a product. There are two types of the product, M1 and M2 available. M1 occupies 2 ft², cost Rs. 12/- and the company makes a profit of Rs. 3/-. M2 occupies 3ft², costs Rs. 15/- and the company makes a profit of Rs 4/- If the budget is Rs. 15,000/- and the warehouse has 3000 ft² for product. Formulate the problem as a linear programming model and solve the problem using simplex method. [8]

--- Content provided by FirstRanker.com ---

2. Solve the following transportation problem, i.e., find the optimal solution, where the entries are cost coefficients. [8]

   	1	2	3	4	Availability
   From 1	15	0	20	10	50
   Origins 2	15	8	11	20	50
   3	0	16	14	18	100
   Requirement	30	40	60	70	200

   OR Four salesmen are to be assigned to four districts. Estimates of the sales revenue is hundred of Rs. for each salesmen are as follows: Give the assignment pattern that maximizes the sales revenue. [8]

   	A	B	C	D
   Salesmen 1	320	350	400	280
   2	400	250	300	220
   3	420	270	340	300
   4	250	390	410	350

3. Find the sequence that minimizes the total elapsed time (in hours) required to complete the following tasks. Each job is processed in the order ABC. [8]

   JOB	1	2	3	4	5	6	7
   Machine A	12	6	5	11	5	7	6
   Machine B	8	9	4	7	8	3	4
   Machine C	3	4	1	5	12	3	4

   OR The mortality rates as obtained for an electronic component are noted in the table below

   Month	1	2	3	4	5	6
   Percentage fails at the end of the month	8	22	14	5	70	85	100

   There are 1500 items in operation. It costs Rs. 20 to replace an individual item and Re.0.50 per item if all items are replaced simultaneously. It is decided to replace all items at fixed intervals and to continue replacing individual item as and when they fail. At what intervals should all items be replaced? [8]
4. The routes of an airline which connects 16 cities (A,B....P) are shown in fig. below. Journey from one city to another is possible only along the lines (routes). Shown with the associated costs indicated on the path segments. If a person wants to travel from city A to City P with minimum costs, without any back tracking, determine the optimal path (route) using dynamic programming. [8] OR A and B play a game in which each has three coins a 5 paise, a 10 paise and a 20 paise. Each selects a coin without the knowledge of the others choice. If the sum of the coins is an odd amount, A wins B's coins. If the sum is even B wins A’s coins. Find the best strategy for each player and the value of the game. [8]
5. The demand of an item is uniform at a rate of 20 units per month. The fixed cost is Rs. 10 each time a production run is made. The production cost is Rs 1 per item and the inventory carrying cost is Rs. 0.25 per item per month. If the shortage cost is Rs. 1.25 per item per month, determine how often to make a production run and of what size should it be? [8] OR A T.V. repairman finds that the time spent on his jobs have an exponential distribution with mean of 30 minutes. If he repairs sets in the order in which they come in, and if the arrival of sets is approximately Poisson distribution with an average rate of 10 per 8 hour day, what is repairmen's expected idle time each day? How many jobs are ahead of the average set just brought in? [8]

---00000-—-

--- Content provided by​ FirstRanker.com ---

FirstRanker.com