Indira Gandhi National Open University (IGNOU) 2005 Diploma Computer Applications CS51 (S) Operations Research - - Question Paper

ADCA / MCA (II Year)
Term-End exam

December, 2005

CS51 (S): Operations Research

Time: three hours
Maximum Marks: 75

Note : ques. number one is compulsory. Attempt any 3 more ques. from ques. numbered two to 5.
1. (a) A manufacturer produces 3 models (I, II and III) of a certain product. She uses 2 kinds of raw materials (A and B) of which 4000 and 6000 units, respectively, are available. The raw material requirements per unit of the 3 models are as follows :

Raw material Requirement per unit of provided Model
I II III
A two three five
B four two seven

The labour time of every unit of Model I is twice that of Model II and 3 times that of Model III. The entire labour force of the factory can produce an equivalent of 2500 units ol Model I. A market survey shows that the minimum demand of the 3 models is : 500, 500 and 375 units, respectively. However, the ratios of the number of units produced must be equal to three : two : 5. presume that the profit per unit of Models I, II and III is Rs. 60, 40 and 100, respectively.
Formulate this issue as an LPP model to determine the number of units of every product which will maximize profit. (6)

(b) List the steps involved in the most general case of the simulation process. (4)

(c) describe the subsequent dynamic programming terms : (6)
(i) Stage
(ii) State Variable
(iii) Decision variable
(iv) Immediate return
(v) Optimal return
(vi) State transformation function

(d) List the major limitations of the PERT model. (4)

(e) Determine the optimal strategies for both the players, and the value of the game, for the subsequent payoff matrix : (6)


Player B 2 -2 four 1Player A six one 12 three -3 two 0 six two -3 seven 1(f) A farmer buys a volume of cabbage seeds from a company that claims that approximately 80% of the seeds will germinate if planted properly. lf four seeds are planted, what is the probability that
(i) exactly 2 will germinate ?
(ii) at lowest 2 will germinate ? (4)

2. (a) A company has factories at F1, F2 and F3, which supply to warehouses at W1, W2 and W3. Weekly factory capacities are 200, 160 and 90 units, respectively. Weekly warehouse requirements are 180, 120 and 150 units, respectively. Unit shipping costs (in rupees) are as follows :

Ware house
Factory W1 W2 W3 Supply
F1 16 20 12 200
F2 14 eight 18 160
F3 26 24 16 90
Demand 180 120 150 450

Determine the optimal distribution for this company to minimize total shipping cost. (8)

(b) every unit of an item costs a company Rs. 40. Annual holding costs are 18 percent of the unit cost for interest charges, one percent tor insurance, two percent allowances for obsolescence, Rs. two for building overheads, Rs. 1.50 for damage and loss, and Rs. four miscellaneous costs. The annual demand for the item is constant at 1000 units and every oder costs Rs. 100 to place.
(i) compute the EOQ and the total costs associated with stocking the item.
(ii) If the supplier of the item will only deliver batches of 250 units, how are the stock holding costs affected ? (7)

3. (a) The trend of demand for a seasonal product is as follows :

Demand (in units) Probability
1 0.05
2 0.10
3 0.15
4 0.20
5 0.20
6 0.15
7 0.10
8 0.05

The cost ot product is Rs. 80 per unit and selling price is Rs. 120. How many units should be purchased for the season so as to maximize expected profit ? Also, if the salvage price of the product is Rs. 20, then would there be any change in the purchase decision ? (7)

(b) In a railway marshalling yard, goods trains arrive at a rate of 30 trains per day. presume that the inter-arrival time follows an exponential distribution, and the service time (ie., the time taken to service a train) distribution is also exponential with an avg. of 36 minutes. compute the
(i) expected queue size (line length);
(ii) probability that the queue size exceeds 10.
If the input of trains increases to an avg. of 33 per day, what will the modifications be in (i) and (ii) ? (8)

4. (a) A man is engaged in buying and selling identical items. He operates from a warehouse having a capacity of 500 items. every month he can sell any volume that he selects up to the stock at the beginning of the month. every month, he can buy as much as he wishes for delivery at the end of the month so long as his stock does not exceed 500 Items.
For the next 4 months he has the subsequent error-free forecasts of cost and sales price :

Month n one two three four
Cost, Cn 27 24 26 28
Sales price, Pn 28 25 25 27

If he currendy has a stock of 200 units, what volumes should he sell and buy in the next 4 months ? obtain the solution using dynamic Programming. (10)

(b) Use the Kuhn - Tucker conditions to solve the subsequent nonlinear programming issue : (5)
Max z = 10x1-x12+10x2-x22
s.t. x1+x2 = 8
-x1+x2 = 5
x1, x2 = 0

5. Solve the subsequent LP issue by using the two-phase method: (15)
Minimize z = x1+x2
s.t. 2x1+4x2 = 4
x1+7x2 = 7
and x1, x2 = 0

Earning:   Approval pending.