Q1. a. What do you mean by linear programming problem? Explain the steps involved in linear programming problem formulation?
Ans. A problem consists of a linear function of variable called objective function subject to set of linear equation or inequalities called constraints, are known as linear programming problem.
In LP model the various parameters namely the objective function coefficients, R.H.S, coefficients of the constraints and resource values are certainly known and their value do not change with time. Thus the profit or cost per unit of product, availability of labour and material, market demand is known with certainty.
Ans. Advantages–
1. It helps in attaining the optimum use of productive factors.
2. It improves the quality of decisions. The individual who makes use of linear programming methods becomes more objective than subjective.
3. It also helps in providing better tools for adjustment to meet changing conditions.
4. It highlights the bottlenecks in the production processes.
5. Most business problems involve constraints like raw materials availability, market demand etc. which must be taken into consideration. Just we can produce so many units of product does not mean that they can be sold. Linear programming can handle such situation also.
Limitations–
1. In some problems objective functions and constraints are not linear. LPP under non linear condition usually results in an incorrect soIution
2. LPP deals with problems that have a single objective. Real life problem may involve multiple objectives.
3. Parameters appearing in the model are assumed to be constant. But in real life situation they are neither constant nor deterministic.
4. It is applicable to only static situations since it does not take into account the effect of time.
5. LPP can not be used efficiently for large scale problems, the computational difficulties are enormous, even when the large digital computer is available.
6. LPP may get fractional valued answers for the decision variables, whereas it may happen that only integer values of the variable are logical.
b. A paper mill produces two grades of paper viz., X and Y. Because of raw
material restrictions, it cannot produce more than 400 tons of grade X paper
and 300 tons of grade Y paper in a week. There are 160 production hours in a
week. It requires 0.20 and 0.40 hours to produce a ton of grade X and Y papers.
The mill earns a profit of Rs. 200 and Rs. 500 per ton of grade X and Y paper
respectively. Formulate this as a Linear Programming Problem.
Q2. a. Discuss the methodology of Operations Research.
b. Explain in brief the phases of Operations Research.
Dear Students,
Get your assignments from Our ESTEEMED ORGANIZATION smumbaassignment.com Just email to kvsude@gmail.com or S M S to +91 9995105420. message Format – SMU MBA <Name> <E-MAIL ID> <SEM ? > To +91 9995105420 , we will reach back you with in 24H Or Directly call our Middle East Office +974 55702886 . More Info, Kindly visit smumbaassignment.com Best Regards, Admin smumbaassignment.com |
Q3. Solve the following Linear Programming Problem using Simple method.
Maximize Z= 3×1 + 2X2
Subject to the constraints:
X1+ X2 ≤ 4
X1+ X2 ≤ 2
X1, X2 ≥ 0
Q4. Explain the procedure of MODI method of finding solution through optimality
test.
Q5. a. Explain the steps in Hungarian method.
b. Solve the following assignment problem.
Machine Operators
1 2 3 5
A 60 50 45 45
B 40 45 55 35
C 55 70 60 50
D 45 45 40 45
Q6. a. Explain the steps involved in Vogel’s approximation method (VAM) of
solving Transportation Problem.
b. Solve the following transportation problem using Vogel’s approximation
method.
Factories Distribution Centres Supply
C1 C2 C3 C4
F1 3 2 7 6 50
F2 7 5 2 3 60
F3 2 5 4 5 25
Requirements 60 40 20 15