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

ADCA / MCA (II Year)
Term-End exam

December, 2005

CS51: 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) describe and provide 1 example, of every of the subsequent : (10)
(i) Economic order volume
(ii) Variance of a distribution
(iii) Feasible region
(iv) Simulation process
(v) Degeneracy

(b) Consider a small plant which makes 2 kinds of automobile parts, say A and B. lt buys castings that are machined, bored and polished. The capacity of machining is 25 per hour for A and 24 per hour for B, the capacity of boring is 28 per hour for A and 35 per hour for B, and the capacity of polishing is 35 per hour for A and 25 per hour for B. Castings for part A cost Rs. two and sell for Rs. five each, and those for part B cost Rs. three and sell for Rs. six every. The 3 machines have running costs of Rs. 20, Rs. 14 and Rs. 17.50 per hour. presume that any combination of parts A and B can be sold. Formulate this issue as an LP model to determine the product mix which maximizes profit. (6)

(c) obtain the range of values of p and q which will render the entry (2, 2) a saddle point for the game. (5)

Player A Player B
B1 B2 B3
A1 two four five
A2 10 seven q
A3 four p six

(d) If S1 and S2 are 2 converse sets, check whether: (4)
(i) S1 n S2 will always be convex.
(ii) S1 ? S2 will always be convex.

(e) List the steps involved in the application of CPM. (2)

(f) The number of cheques processed by a bank every day is normally distributed with a mean of 30,100 and standard deviation of 2450. obtain the probability that the bank processes more than 32,000 cheques in a day. (3)
[Note that P[0 to 0.22] = 0.0871,
P[0 to 0.78] = 0.2823, and
P[0 to 1.78] = 0.4625

2. Use the Big-M method to solve the subsequent LP issue. (15)
Maximize z=x1+2x2+3x3-x4
s.t.
x1+2x2+3x3 = 15
2x1+x2+5x3 = 20
x1+2x2+x3+x4 = 10
and x1,x2,x3 = 0

3. (a) A city corporation has decided to carry out road repairs on the 4 main roads of the city. The government has agreed to make a special grant of Rs. 50 lakhs towards the cost with the condition that the repairs be done at the least cost and quickest time. lf the conditions warrant, a supplementary token grant will also be considered favourably. The coporation has floted tenders and 5 contractors have sent in their bids. In order to expedite work, 1 road wiil be awarded to only 1 contractor.

Cost of Repairs (Rs. lakh)

Road R1 R2 R3 R4 C1 nine 14 19 15 C2 seven 17 20 19Contractors C3 nine 18 21 18 C4 10 12 18 19 C5 10 15 21 16(i) obtain the best way of assigning the repair work to the contractors and the cost.
(ii) If it is necessary to seek supplementary grants, what amount should be asked for ? (7)

(b) A road transport company has 1 reservation clerk on duty at a time. She handles info of bus schedules and makes reservations. Customers arrive at a rate of eight per hour and the clerk can service 12 customers on an avg. per hour, Alter stating your assumptions, ans the following:
(i) What is the avg. number of customers waiting for the service of the clerk ?
(ii) What is the avg. time a customer has to wait before getting service ?
(iii) The management is thinking of installing a computer system to handle the info and reservations. This is expected to decrease the service time from five to three minutes. The additional cost of having the new system works out to Rs. 50 per day. lf the cost of goodwill of having to wait is estimated to be 12 paise per minute spent waiting before being served, should the company install the computer system ? presume an 8-hour working day. (8)

4. (a) Suppose there are n machines which can perform 2 jobs. If x of them do the 1st job, then they produce goods worth g(x) = 3x, and if y of them perform the 2nd job, then they produce goods worth h(y) = 2.5y. Machines are subject to depreciation. So, after performing the 1st job only a(x) = x/3 machines remain unavailable and after performing the 2nd job b(y) = 2y/3 machines remain available in the beginning of the 2nd year. The process is repeated with the remaining machines. find the maximum total return after 3 years, and also obtain the optimal policy in every year. (9)

(b) Solve the game whose payoff matrix is provided beneath : (6)


B1 B2 B3 A1 30 40 -80 A2 0 15 -20 A3 90 20 505. (a) The production department for a company requires 3600 kg of raw material for matufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs.36 and the cost of inventory carrying is 25 percent of the investment in the inventories. The price is Rs. 10 per kg. Determine an ordering policy for the raw material. (8)

(b) Derive the Kuhn - Tucker condition for the subsequent problem, and obtain the value of x1 and x2 for which these conditions are satisfied.
Max z = 10x1-x12+10x2-x22
s.t. x1+x2 = 14
-x1+x2 = 6
and x1, x2 = 0 (7)

Earning:   Approval pending.