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Name of the Institute : Babu Banarasi Das National Institute of Technology & Management
Degree : BCA
Department : Computer Applications
Subject Code/Name : (BCA-505) Optimization Techniques
Year : 3rd
Semester : 5th
Document Type : Question Bank
Website : bbdnitm.ac.in

Download Model/Sample Question Paper :https://www.pdfquestion.in/uploads/bbdnitm.ac.in/3174-BCA-C-505-OT-QUESTION-BANK.pdf

BBDNITM Optimazation Techniques Question Paper

Unit – I

1. A firm manufactures 3 products A, B and C. The profits are Rs. 3, Rs. 2 and Rs. 4 resp. The firm has 2 machines and below is the required processing time in minutes for each machine on each product. Machine G and H have 2000 and 2500 machine-minutes resp. The firm must manufacture 100 A’s, 200 B’s and 50 C’s, but no more than 150 A’s. Formulate an LPP to maximize profit.

Related : BBDNITM BCA502 Internet Technology & Applications BCA Question Bank : www.pdfquestion.in/3171.html

2. A farmer has 100 acre farm. He can sell all tomatoes, lettuce or radishes he can raise. The price he can obtain is Re. 1.00 per kg for tomatoes, Rs. 0.75 a head for lettuce and Rs. 2.00 per kg for radishes. The average yield per acre is 2000 kg of tomatoes, 3000 heads of lettuce, and 1000 kg of radishes. Fertilizer is available at Rs. 0.50 per kg and the amount required per acre is 100 kg each for tomatoes and lettuce, and 50 kg for radishes. Labour required for sowing, cultivating and harvesting per acre is 5 man-days for tomatoes and radishes, and 6 man-days for lettuce. A total of 400 man-days of labour are available at Rs. 20.00 per man-day. Formulate this problem as a LPP to maximize the farmer’s total profit.

3. A firm plans to purchase at least 200 quintals of scrap containing high quality metal X and low quality metal Y. It decides that the scrap to be purchased must contain at least 100 quintal of X-metal and not more than 35 quintals of Y-metal. The firm can purchase the scrap from two suppliers (A and B) in unlimited quantities. The percentage of X and Y metals in terms of wt. in the scraps supplied by A and B is given below : The price of A’s scrap is Rs. 200 per quintal and that of B’s is Rs. 400 per quintal. Formulate this problem as LPP and solve it to determine the quantities that the firm should buy from the two suppliers so as to minimize total purchase cost.

4. Write any four limitations of Linear Programming.
5. What are the advantages of two-phase method over Big-M method?

Unit – II

1. Determine the initial basic feasible solution of the following transportation problem using North-West Corner method,
2.Determine the initial basic feasible solution of the following transportation problem using Row-minima method :

3. Obtain the initial basic feasible solution of the following transportation problem using matrix-minima method : D1 D2 D3 D4 Supply O1 1 2 3 4 6 O2 4 3 2 0 8 O3 0 2 2 1 10 Demand 4 6 8 6

4. Obtain the initial basic feasible solution of the following transportation problem using Vogel’s method : D1 D2 D3 D4 Supply O1 21 16 15 13 11 O2 17 18 14 23 13 O3 32 27 18 41 19 Demand 6 10 12 15

5. Find the optimum solution to the following TP : A B C D E Supply 1 3 4 6 8 8 20 2 2 10 1 5 30 30 3 7 11 20 40 15 15 4 2 1 9 14 18 13 Demand 40 6 8 18 6

6. The unit cost of transportation from site I to site J is given below. At site i=1,2,3, stocks of 150, 200, 170 units resp., are available. 300 units are to be sent to site 4 and rest to site 5. Find the cheapest way of doing this.

7. A Deptt. Head has 4 subordinates, and 4 tasks have to be performed. Subordinates differ in efficiency and tasks differ in their intrinsic difficulty. Time each man would take to perform each task is given in the effectiveness matrix. How the tasks should be allocated to each person so as to minimize the total man-hours?

9. A team of 5 horses and 5 riders has entered a jumping show contest. The no. of penalty points to be expected when each rider rides any horse is shown below : How should the horses be allotted to the riders so as to minimize the expected loss of the team?
10. Solve the following cost-minimizing problem :

11. A manufacturer of baby dolls makes 2 types of dolls : doll x and doll y. processing of these dolls is done on 2 machines A and B. doll X requires 2 hrs. on A and 6 hrs. on B. Doll Y requires 5 hrs. on A and 5 hrs. on B. There are 16 hrs. of time per day available on A and 30 hrs. on B. The profit gained on both the dolls is same, i.e. 1 Re. per doll. What should be daily production of each of the 2 dolls? Solve the LPP and if the optimal solution is not integer valued, use Gomory’s technique to derive the optimal solution.

12. Write the applications of Integer Programming.

Unit – III

1. The total profit of a restaurant was found to depend mostly on the amount of money spent on advertising and the quality of the preparation of the food(measured in terms of the salaries paid to the chefs). In fact the manager of the restaurant found that if he pays his chefs x Rs. Per hr. and spends Rs. Y a week on advertising., the restaurant’s weekly profit (in Rs.) will be Z= 412x+806y-x2-y2-xy. What hourly wages should be the manager pay his chefs and how much should he spend on advertising so as to maximize the restaurant’s profit?

2. Derive Kuhn-Tucker necessary conditions for an optimal solution to a quadratic prog. problem.
3. What is Quadratic Programming? Explain Wolfe’s method of solving it.
4. Mention briefly the Wolfe’s algorithm for solving a quadratic PP given in the usual notations :
5. What is meant by Quadratic Programming? How does quadratic programming problem differ from the LPP?

Unit – IV

1. There are 6 jobs to be performed each of which should go through 2 machines A and B in the order A, B. The processing times (in hrs.) for the jobs are given :
Jobs : 1 2 3 4 5 6
Machine A : 1 3 8 5 6 3
Machine B : 5 6 3 2 2 10
Determine the sequence for performing the jobs that would minimize the total elapsed time T. What is T?

2. Find the sequence that minimizes the total elapsed time required to complete the following jobs on two machines.
Jobs : J1 J2 J3 J4 J5 J6 J7 J8 J9
Machine A : 2 5 4 9 6 8 7 5 4
Machine B : 6 8 7 4 3 9 3 8 11

3. Find the sequence that minimizes the total elapsed time required to complete the following jobs on three machines in order of ABC.
Jobs : J1 J2 J3 J4 J5
Machine A : 8 10 6 7 11
Machine B : 5 6 2 3 4
Machine C : 4 9 8 4 5

4. Use graphical method to minimize the total elapsed time needed to process the following jobs on machines shown :
Job 1 : Sequence : A B C D E
Time (hrs.) : 3 4 2 6 2
Job 2 : Sequence : B C A D E
Time : 5 4 3 2 6

5. A salesman estimates that the following would be the cost on his route visiting the 5 cities as shown in the table below Determine the optimal route.

6. A salesman has to visit 5 cities A, B, C, D and E. The distances (in hundred miles) between 5 cities are as follows. If the salesman starts from city A and back to city A, which route should he select so that the total distance traveled is minimum?
8. Solve the following sequencing problem giving an optimal solution when passing is not allowed.

9. Find the optimal solution of the following sequencing problem :
10. A company is producing a batch of 5 parts A,O, E, N and L using 3 machines X,W,M. All these parts are to be produced in the technological order X,M,W machines. Processing times are as follows. Find the optimum sequence of jobs and machine utilization percentages for each machine.

11. Write Johnson’s algorithm for n jobs and 2 machines.
12. A company has 6 jobs on hand A to F. All jobs have to go through 2 machines M1 and M2. The time required for each job on each machine in hrs. is given below :
A B C D E F
M1 : 3 12 18 9 15 6
M2 : 9 18 24 24 3 15
Draw a sequence table of 6 jobs on 2 machines.

13. 2 jobs are to processed on 4 machines A,B, C, D. The technological order for these machines is as follows :
Job 1 : Sequence : A B C D
Time : 4 6 7 3
Job 2 : Sequence : D B A C
Time : 6 4 2 3
14. Find the sequence that minimizes the total elapsed time :
A B C D E F G H I
M1 : 2 5 4 9 6 8 7 5 4
M2: 6 8 7 4 3 9 3 8 11

15. There are 5 jobs each of which must go through machines A,B,C in order ABC. Processing times are given below. Determine a sequence of given jobs that will minimize the total elapsed time T.

Unit – V

1. Write short notes on
i) CPM
ii) PERT
2. Derive economic order quantity model for an inventory problem when shortages are not allowed.

3. An aircraft company uses rivets at an approximate customer rate of 2500 kg. per year. Each unit costs Rs. 30 per kg. and the company personnel estimate that it costs Rs. 130 to place an order, and that the carrying cost of inventory is 10% per year.
i) How frequently should orders for rivets be placed? Also determine the optimum size of each order.
ii) If the actual costs are Rs. 500 to place an order and 15% for carrying cost, the optimum policy would change.How much is the company losing per year because of imperfect cost information?
4. If the setup cost instead of being fixed fixed is equal to (C3+Bq), where B is the setup cost per unit time produced, then show that there is no change in the optimum order quantity produced due to this change in the setup cost.
5. Given the following data for an item of uniform demand, instantaneous delivery time and back order facility : Annual Demand =800 units, cost of an item=Rs. 40, ordering cost=Rs. 800, inventory carrying cost=40%, back order cost=Rs.10.
Find
i) minimum cost order quantity
ii) maximum no. of back orders
iii) maximum inventory level
iv) time between two consecutive orders
v) total annual cost
6. Consider the inventory system with the following data : R=1000 units/year, I=0.30, P=Rs. 0.50 per unit, C3=Rs. 10, L=2 yrs. Determine optimal order quantity , reorder point, minimum average cost.
7. Formulate and solve a mathematical model for all units discounts when shortages are not allowed to obtain the optimal value of the order quantity.
8. Find the optimum order quantity for a product for which the price breaks are as follows :
Quantity : 0<=q1<500 q2>=500
Unit cost(Rs.) : 15.00 14.50
Monthly demand for the product is 250 units , cost of storage is 2% of the unit cost and ordering cost is Rs. 300.
9. Find the optimum order quantity for a product for which the price breaks are as follows :
Quantity : 0<=q1<50 50<=q2<100 100<=q3
Unit cost(Rs.) : 10.00 9.00 8.00
Monthly demand for the product is 200 units , cost of storage is 25% of the unit cost and ordering cost is Rs. 20 per order.
10. Write short notes on
i) Types of inventory
ii) Inventory decisions
11. What do you understand by network scheduling? Differentiate between PERT and CPM?
12. What is a float? Give its type and find the floats for the following activity of a certain network.
E1=20 E2=39
L1=38 L2=57
13. Give the concept of Economic order quantity? Also give formulae for different situations?
14. A project consists of a series or tasks labeled A,B,…,H, I with the following relationships(W<X,Y, means X cannot start until W is completed; X,Y<W means W cannot start until both X and Y are completed). With this notation, construct the network diagram having the following constraints :
A<D,E;B,D<F;C<G;B<H;F,G<I
Find also the optimum time of completion of the project, when the time (in days) of completion of each task is as follows:
Task: A B C D E F G H I
Time: 23 8 20 16 24 18 19 4 10
15. Find the critical path and calculate the slack time for each event for the following PERT diagram.