- All questions are compulsory in section I and
- Attempt any 3 from section II
- Normal distribution table is attached.

Section I

Q.1) answer the following questions briefly (15)

a) What are the components of formulation of linear programming problems?

b) What is an assignment problem? How will you deal with assignment problem where some assignments are prohibited?

c) Name any 3 methods of finding initial basic feasible solution for the transportation problems. Which one of them is best and why?

d) Distinguish between PERT and CPM network. Give one application of CPM network

e) What are the objectives of project crashing?

Q.2) from the following data, determine:-

I. Normal project duration and cost

II. Optimal project completion time and cost

Activity 1-2 1-3 3-5 3-6 2-4 2 -5 4-5 4-6 5-6

Normal time(week) 3 8 6 5 4 13 2 2 6

Normal cost (Rs.) 1800 60 1000 400 1500 300 120 700 350

Crash time (weeks) 2 6 4 2 4 10 1 1 4

Crash cost (Rs.) 1900 100 1200 1000 1500 900 140 800 450

The indirect cost of the project is Rs.90/week

If it is necessary to complete the project in 17 weeks, at what cost it could be achieved ?

Section II

Q.3) a company which manufactures three products A,B and C requiring two resources labor and materials and want to determine the optimal product mix that maximizes profit the following linear program was formulated to answer this:-

Maximize Z = 3 X_{1} + X_{2}+5X_{3}

Subject to 6x_{1}+3x_{2}+5X_{3 }<=45 (labor)

3X_{1}+4X_{2}+5X_{3 }<=30 (material)

Where x_{1}, x_{2}, x_{3} are the units of products A, B, C product. Find the optimum product mix. (10)

Q.4) the Indian navy wishes to assign 4 ships to patrol 4 sectors of the sea. In some areas ships are to be on the lookout for illegal fishing boats, and in other sectors to watch for enemy submarines, so the commander rates each ship in terms of its probable efficiency in each sector. These relative efficiencies are given in the table below:-

Ship | A | B | C | D |

1 | 20 | 60 | 50 | 55 |

2 | 60 | 30 | 80 | 75 |

3 | 80 | 100 | 90 | 80 |

4 | 65 | 80 | 75 | 70 |

On the basis of the rating shown , the commander wants to determine the patrols assignments producing the greatest over all efficiencies what is the optimal assignment ? (10)

Q.5) given elow is a table taken from the solution process for a transportation problems.

Cost per unit (in Rs.)

Distribution centre

factory |
1 |
2 |
3 |
4 |
availability |

A |
10 |
8 5000 |
7 |
12 |
5000 |

B |
12 |
13 |
6 4500 |
10 1500 |
6000 |

C |
8 7000 |
10 500 |
12 |
14 1500 |
9000 |

Demand |
7000 |
5500 |
4500 |
3000 |

Answer the following question and answer briefly

a) Is this solution feasible?

b) Is this solution degenerate?

c) Is the solution optimum? If not find the optimum solution.

d) Does the problem have alternative optimum solutions?

Q.6) a farm owner is considering drilling a well. In the past only 85% of the wells had yielded water at a depth of 250 feet in the area. On the finding, no water at a depth of 250feets some persons drilled further down up to 300 feet but only 25% struck water at the depth. The cost of drilling Is Rs.35/foot. The farmer estimates that if he does not have his own well he will be have to pay Rs.15000 over the next 10yrs.(in PV terms) to buy water from a neighbor. The following decision could be optimal.

a) Do not drill a well

b) Drill up to 250 feet

c) If no water is found at 250 feet drill upto 300 feet

d) Draw a decision tree to represent the situation and determine the farm owner’s strategy under the EMV approach (10)

activity | Three time (estimated week) |

1-2 | 1-1-7 |

1-3 | 1-4-7 |

1-4 | 2-2-8 |

2-5 | 1-1-1 |

3-5 | 2-5-14 |

4-6 | 2-5-8 |

5-6 | 3-6-15 |

Draw the project network

a) Find the expected duration and variation for each activity.

b) Find SD of project length

c) What is the probability that the projected will be completed in 20 weeks or less?

d) What should be the project due date so that probability of achieving it is 95%