Assignment Problems
on Operations Research
1. Old hens can be bought for Rs. 2.00 each but young one costs Rs. 5.00 each. The old hens lay 3 eggs per week and
young ones 5 eggs per week, each egg being worth 30 paise. A hen costs Rs. 1.00 per week to feed. If I have only
Rs. 80.00 to spend for purchasing the hens , how many of each kind should I buy to have a maximum profit per
week assuming that I cannot house more than 20 hens?
What additional constraint is to be added to the constraint set in order that the profit
will be more than Rs. 6.00 per week? [Ans. 16 young hens only;Max. profit = Rs. 8.00;0.5x2 – 0.1x1 6.]
2. A firm , manufacturing two types of medicines A and B , can make a profit of Rs. 20 per bottle of A and Rs. 30 per
bottle of B. Both A and B need for their production two essential chemicals C and D. Each bottle of A requires 3
litres of C and 2 litres of D and each bottle of B requires 2 litres of C and 4 litres of D. The total supply of these
chemicals is 210 litres of C and 300 litres of D. Type B medicine contains alcohol and its manufacture is restricted
to 65 bottles per month. How many bottles each of A and B should the firm manufacture per month to maximize its
profit of the products? How much is this profit? [Ans. 30 bottles A type a nd 60 bottles B type. The profit is Rs.
2400.]
3. A business man has the option of investing his money in two plans. Plan A guarantees that each rupee invested will
earn seventy paisa a year hence, while plan B guarantees that each rupee invested will earn two rupees two years
hence. In plan B, only investments for periods that are multiples of two years are allowed. The problem is how he
should invest ten thousand rupees in order to maximize the earnings at the end of three years. Formulate this
problem as a linear programming model.
Solve the following L.P.P. by simplex method(4-7).
5. Maximize z 4x1 7 x 2
4. Maximize z 2 x1 3x 2
Subject to 2x1 x 2 1000 ,
Subject to x1 x2 1
10 x1 10 x 2 6000 ,
3x1 x 2 4,
2x1 4x 2 2000 ,
x1, x 2 0, x1, x 2 0,
[Ans. x1 0, x 2 1; z max 3.] [Ans. x1 200, x 2 400 ; z max 3600 .]
Check the results of Problems 4 and 5 graphically.
6. Maximize z = 3x1 x 2 3x3 Minimize 7. Minimize z = x1 3x2 2x3
Subject to 2x1 x 2 x3 2, Subje Subject to 3x1 x 2 2x3 7,
x1 2x 2 3x3 5, 2x 1 4x 2 12,
2x1 2x 2 x3 6, 4x1 3x 2 8x3 10,
x 1, x 2 , x 3 0. x 1, x 2 , x 3 0.
1 8
[Ans. x1 5 , x 2 0, x3 5 ; zmax 27
5. ] [Ans. [Ans. x1 4, , x 2 5, x3 0; zmin 11.]
8. Solve the following L.P.P. by any method.
Maximize z = 7x1 3x 2
9. Use Charnes Big - M method to
Subject to x1 +2 x 2 3 , Maximize z 3x1 x 2
x1 x 2 4, Subject to 2x1 x 2 2,
x1 52 ,
x1 3x 2 3,
x2 4,
x1, x 2 0,
[Ans. x1 3, x 2 0; z max 9.]
x 2 32 ,
x1, x 2 0.
[Ans. x1 5 2, x 2 3 2 ; zmax 22. ]
10. Use Charnes Big - M method to 11. Use Charnes Big - M method (method of penalty ) to
Maximize z x1 5x 2 Maximize z = 5x 1 2x 2 3x 3
Subject to 3x1 4x 2 6, Subject to 2x 1 x 2 x 3 2,
x1 3x 2 3, 3x1 4x 2 3,
x1, x 2 0, x 2 3x 3 5,
[Ans. x1 0, x 2 3 2 ; z max 15 .]
2 x 1, x 2 , x 3 0.
[Ans. x 1 23 3 , x 2 5, x 3 0; z max 85
3.]
Use the Two-Phase simplex method to solve the following L.P.P.(12-13).
12. Maximize z 5x1 3x 2 13. Maximize z 5x1 8x 2
Subject to 3x1 5x 2 15, Subject to 3x1 2x 2 3,
5x1 2x 2 10, x1 4x 2 10,
x1, x 2 0, x1 x 2 5,
[Ans. x1 20 19 , x 2 45 19 ; z max 235 x1, x 2 0,
19 .]
[Ans. x1 0, x 2 5; z max 40.
