PART-A
UNIT-1
1. What is operations research?
2. Define a feasible region.
3. Define a feasible solution.
4. Define optimal solution.
5. What is the difference between feasible solution and basic feasible solution?
6. Define unbounded solution.
7. What are the two forms of a LPP?
8. What do you mean by standard form of LPP?
9. What do you mean by canonical form of LPP?
10. What are the limitations of LPP?
11. What are the slack and surplus variables?
12. What is meant by optimality?
13. Define artificial variable.
14. What are the methods used to solve an LPP involving artificial variables?
15. What is degeneracy?
PART-B
UNIT-I
LINEAR PROGRAMMING(LP)
1. (a) Explain the scope of OR.
(b) List the phases of OR and explain them.
(8)
(8)
2. (a) A company wishes to advertise its products on local radio and TV stations. Each
minute of radio advertisement will cost Rs.50 and each minute of TV
advertisement will cost Rs. 600. The budget of the company limits the
advertisement expenditure to Rs.25000 per month. The company decides to use
radio atleast twice as much as TV. Past records of the company show that each
minute of TV advertisement will generate 30 times as many sales as each minute
radio advertisement. Formulate the problem for optimal allocation of monthly
budget to radio and TV advertisement.
(8)
(b) A paper mill produces 2 grades of paper namely X and Y. Because of raw
material restrictions, it cannot produce more than 400 tonnes of grade X and 300
tonnes of grade Y in a week. There are 160 production hours in a week. It
requires 0.2 and 0.4 hours to produce a ton of products X and Y respectively with
corresponding profits of Rs.200 and Rs. 500 per ton. Formulate the above as a
LPP to maximize profit and find the optimum product mix.
(8)
3 (a) A company produces 2 types of hats. Every hat A require twice as much labour
time as the second hat be. If the company produces only hat B then it can
produce a total of 500 hats a day. The market limits daily sales of the hat A and
hat B to 150 and 250 hats. The profits on hat A and B are Rs.8 and Rs.5
respectively. Solve graphically to get the optimal solution.
(8)
(b) Use graphical method to solve the LPP
Maximize Z = 2x1+4x2
Subject to the constraints
x1+2x2 ≤ 5,
x1+x2≤4,
x1, x2≥ 0
(8)
4 Use simplex method to solve the following LPP
Maximize Z = 4x1+10x2
Subject to the constraints
2x1+x2 ≤ 50,
2x1+5x2 ≤100,
2x1+3x2 ≤90,
x1, x2 ≥ 0
(16)
5. Solve the following problem by simplex method
Minimize Z = x1-3x2+2x3
Subject to the constraints
3x1-x2+2x3 ≤ 7,
-2x1+4x2≤12,
-4x1+3x2+8x3 ≤ 10,
x1, x2, x3 ≥0
6. Use Big M method to
Maximize Z = 3x1+2x2
Subject to the constraints
2x1+x2 ≤ 2,
(16)
3x1+4x2 ≥12,
x1, x2 ≥0
(16)
7. Use Penalty method to
Maximize Z = 6x1+4x2
Subject to the constraints
2x1+3x2≤ 30,
3x1+2x2 ≤ 24
x1+x2≥ 3,
x1, x2≥ 0
(16)
8. Use Two Phase Simplex method to
Maximize Z = 5x1-4x2+3x3
Subject to the constraints
2x1+x2-6x3 = 20,
6x1+5x2+10x3 ≤76,
8x1-3x2+6x3 ≤ 50,
x1, x2, x3≥ 0
(16)
9. Use Two Phase Simplex Method to
Maximize Z = -4x1-3x2-9x3
Subject to the constraints
2x1+4x2+6x3≥ 15,
6x1+x2+6x3 ≥12,
x1, x2, x3≥ 0
(16)