**Pokhara UniversitySemester-springLevel: Master Year: 2016Program: MCISFull Mark: 100Course: Operation research Pass Mark: 60 **

**1. A furniture company produces two types of products chair and table. The profit contribution on each chair is rs.4oo and on each table is rs.320. The company can sell all the chairs or all the tables or any combination of tables and chairs that it can produce. Unfortunately the production capabilities are severely restricted in several respects. First, a special wood, which is used as a primary raw material in producing both chairs and table, is available only in very limited quantities. The labor of highly skilled nature is required in wood working process and also in finishing process. Both types of labor are in scare supply, so company can produce only limited quantities of chairs and tables. Each chair requires in its construction 20 unit of special wood, while each table requires 10 units and maximum quantity of special wood available is 300 units, only 100 man hours of wood working are available. Each chair required 4 hours of wood working labor and10 hours of wood working labor is required to produce one table. The final step in the production process, finishing work is also ;performed by highly skilled labor and a maximum of 38 man hours of this finishing labor is available. Each chair requires 2 man-hours and each table requires three man-hours of finishing time .Formulate a linear programming model and determine how much of each product should be manufactured to maximize total profit contribution by using graphical method.**

**2. An advertising agency wishes to reach two types of audiences: Customer with annual income greater than Rs 15,000(target audience A) and customers with annual income less than Rs 15,000(target audience B).The total advertising budget is Rs 2,00,000. One program me of TV advertising costs Rs 50,000; one programme on radio advertising costs Rs 20,000. For contract reasons, at least three programs ought to be on TV,and the number of radio programmes must be limited to five. Surveys indicate that a single TV programme reaches 4,50,000 customers in target audience A and 50,000 in target audience B. One radio programme reaches 20,000 in target audience A and 80,000 in target audience B. Determine the media mix to maximize total reach by simplex method.**

3. Find the Dual of following LPP:

Max Z= 5X1+10X2+15X3

Subject to constraints

X1+2X2+X3<=40

2X1+X2+6X3>=180

3X1+2X2+3X3=80

X1,X2,X3>=O

4. A department of a company have five employees with five jobs to be performed. The time(in hrs) that each man takes to perform each job is given in effectiveness matrix.

Employees

How should the jobs be allocated, one per employee, so as to minimize the total man-hours?

5. Sunway transport company ships truckloads of grain from three silos to four mills .the supply (in truckloads) and the demand (also in truck laods) together with the unit transportation costs per truckloads on the different routes are in the table. The unit transportation costs,c_{ij} are in hundred of dollars.

Solve the transportation model, starting with the Northwest- corner solution and find its optimality.

**6. Following table lists the activity of a project along with their time estimates.**

Activity |
Predecessor |
Most likely |
optimistic |
pessimistic |

A |
— |
5 |
4 |
6 |

B |
— |
12 |
8 |
16 |

C |
A |
5 |
4 |
12 |

D |
B |
3 |
1 |
5 |

E |
D,A |
2 |
2 |
2 |

F |
B |
6 |
4 |
8 |

G |
C,E,F |
14 |
10 |
18 |

H |
G |
20 |
18 |
34 |

a) Draw network diagram

b) Find expected duration and variance of each activity.

c ) What is the expected project length?

d) Calculate standard deviation and variance of project length.

e) What is the probability that project will completed at least 4 day prior than expected time?

f ) What should be schedule completion time for the probability of completion to be 99%?

**7. Solve the following LPP by revised simplex algorithm.**

Max Z=2X1+4X2+3X3

Subject to constraints

X1+3X2+2X3=20

X1+5X2>=10

X1,X2,X3>=o

**8. Solve the following all-integer linear programming problem by branch and bound method.**

Max Z=3×1+5×2

subject to constraints

2×1+4×2<=25

X1<=8

2×2<=10

X1 and x1 are non negative integer.

**Or**

**What is dynamic programming? solve the bounding problem by recursive method of dynamic programming.**