1) A plant manufactures the washing machines and the dryers. The main manufacturing departments include the stamping department, motor and assembly department and transmission department. The 1st two departments manufacture the parts for both products however the assembly lines are different for two products. The monthly department capacities are as follows:
Stamping department : 1000 washers or 1000 dryers
Motor and transmission department : 1600 washers or 7000 dryers
Washer assembly line : 9000 washers only
Dryer assembly line : 5000 dryers only
Profits per piece of the washers and dryers are Rs.270 and Rs.300 respectively Evaluate the L.P.Model.
2) Evaluate the following L.P problem graphically:
max z = 8000x_{1} + 7000x_{2}, subject to 3x_{1}+ x_{2} ≤ 66, x_{1 }+ x_{2 }≤ 45, x_{1}≤20, x_{2}≤40 and x_{1},x_{2}≥0.
3) Use the dual simplex technique in order to maximize z = 3x_{1}  2x_{2} subjected to the
x_{1}+x_{2}≥1, x_{1}+x_{2}≤7, x_{2}+2x_{2}≥10, x_{2}≤3≤ x_{1},x_{2}≥0.
4) Evaluate the following problem by the Big M=Method:
max z = x_{1} + 2x_{2} + 3X_{3}  x_{4}, subjected to
x_{1} + 2x_{2} + 3x_{3} = 15, 2x_{1} + x_{2} + 5x_{3} = 20, x_{1} + 2x_{2} + x_{3}+x_{4} = 10 and x_{1, }x_{2}, x_{3}, x_{4} ≥ 0.
5) Solve the following given transportation problem:
Destinations

Source

1
2
3

1

2

3

4

Availability

21

16

25

13

11
13
19


17

18

14

23

32

27

18

41

6

10

12

15

43

Requirement
