1.
UNIT-I
b) By applying simplex method find the value of x1, x2Compare the solution with
graphical method solution.
Max Z =5 x1 + 3 x2
[10M]
ST 3x1 + 5x2 ≤ 15
5x1 + 2x2≤ 10, x1 x2 ≥0
2. Solve the following problem using simplex method. Compare the solution with graphical
method solution.
[10M]
Minimize Z = 5x + 4y
Subject to 4x + y ≥ 40
2x + 3 y ≥ 90 and x, y ≥ 0.
3.
a) What are the essential characteristics of a linear programming model?
b) Solve the following L.P problem using simplex method.
Max Z = x1 + x2
[3M]
[7M]
Subject to 2x1 + x2 ≥ 4
x1 + 7x2≥ 7
x1 x2 ≥ 0
4.
a) What is a model? State various models in operation research?
[2M]
b) Minimize the function given below by formulating the dual.
[8M]
Minimize C = 8x + 5y
Subject to constraints
20x + 12y ≥ 200
8x ≥ 40
6y ≥ 30
x≥ 0 and y ≥ 0
5.
a) What are the characteristics and phases of operations research.
[3M]
b) Old hens can be brought at Rs 20 each and young ones at Rs 50 each. The old hens lay 3
eggs per week and the young ones lay 5 eggs per week, each egg being worth of Rs 1.50ps.
a hen(young or old) costs Rs 1.50 per week to feed, I have only Rs 800 to spend for hens,
how many of each kind should I buy to give a profit of at least Rs 60/- per week, assuming
that I cannot house more than 20 hens.[7M]
6.
a) Explain the principles used in formulation for conversion of primal-dual forms of
simplex. Give examples.
[3M]
b) Solve by using Big M method to solve the following LPP.
Max z = -2x1-x2
Subjected to 3x1+ x2 = 3
4x1 + 3x2  6
x1 + 2x2  4
x1, x2 ≥ 0
7. Solve the following LPP graphically:
Maximize Z = 2x1 + 3x2
Subject to:
x1 + x2  1
5x1 - x2  0
x1 + x2  6
x1 - 5x2  0
x2 - x1  -1
x2  3
x1, x2  0
[7M]
8. Use duality to solve the LPP
Minimize z = 8x1 - 2x2 - 4x3
Subjected to
x1 - 4x2 - 2x3  2
x1 +x2 - 3x3  - 1
-3x1 - x2 + x3  -1
x1, x2, x3  0.
9. A farmer has 100 acre farm. He can sell all tomatoes, lettuce, or radishes he can raise. The
price he can obtain is Rs 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
kgs of radishes. Fertilizer is available at Rs 0.50 per kg and the amount required per acre is 100
kgs each for tomatoes and lettuce, and 50 kgs for radishes. Labour required for sowing 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 as a LinearProgramming model to maximize the formers total profit.
10. A company produces two types of leather belts say A and B. Belt A is of superior quality and
B is inferior. Profits on the two are 40 and 30 paisa per belt, respectively. Each belt of type A
requires twice as much time as required by a belt of type B. If all the belts were of type B, the
company could produce1000 belts per day. But the supply of leather is sufficient only for 800
belts per day. Belt A requires a fancy buckle and only 400 of them are available per day. For belt
B only 700 buckles are available per day. Solve this problem to determine how many units of the
two types of belts the company should manufacture in order to have a maximum overall profit?