Operations Research Answers

has decided to carry out road repairs on main four arteries of the Administration. The government has agreed to make a special grant of birr 50 million towards the cost with the condition that the repair must be done at the lowest cost and quickest time. If conditions warrant, then the supplementary token grant will be considered favorably. The Administration has floated the bid and 5 contractors have submitted their bids. In order to expedite their work, one road will be awarded to only one contractor.

Cost of repairs in millions

Contractors R1 R2 R3 R4

C1 9 14 19 15

C2 7 17 20 19

C3 9 18 21 18

C4 10 12 18 19

C5 10 15 21 16

Required:

a) Find the best way of assigning the repair work to the contractors and costs(4pts)

b) If it is necessary to seek supplementary grants, then what should be the amount sought? (3pts)

c) Which of the five contractors will be unsuccessful in this bid (2pts)

has decided to carry out road repairs on main four arteries of the Administration. The government has agreed to make a special grant of birr 50 million towards the cost with the condition that the repair must be done at the lowest cost and quickest time. If conditions warrant, then the supplementary token grant will be considered favorably. The Administration has floated the bid and 5 contractors have submitted their bids. In order to expedite their work, one road will be awarded to only one contractor.

Cost of repairs in millions

Contractors R1 R2 R3 R4

C1 9 14 19 15

C2 7 17 20 19

C3 9 18 21 18

C4 10 12 18 19

C5 10 15 21 16

Required:

a) Find the best way of assigning the repair work to the contractors and costs(4pts)

b) If it is necessary to seek supplementary grants, then what should be the amount sought? (3pts)

c) Which of the five contractors will be unsuccessful in this bid (2pts)

A bakery can produce two kinds of biscuits. The direct costs are RS 30 and RS 50 while the sale price are RS 50 per dozen and RS 8

70 per dozen respectively. Total oven capacity is 80dozen biscuits in all. Making one dozen biscuits requires0.1 and 0.2 hours of labour respectively for two kinds of biscuits. Total labour time available is10 hours. Formulate the above problem as a, LLP and solve it graphically.

Embolot construction project consists of the following activities with duration in weeks of each activity given in brackets. A(8), B(7) and C(10) can be executed concurrently. A and B precede D(3). B precedes E(1) and F(9). F and C precede G(5) and H(7). E and G precede J(3). H precedes K(3). D, J and K precede L(4). L is the terminating activity in the project.

a)     Construct the precedence table and hence draw the network diagram for the project.

A furniture manufacturer makes two products - tables and chair. Processing of these products is done on two types of machine A and B. A chair requires 2 hours on machine type A and 6 hours on machine type B. A table requires 5 hours on machine type A and no hours on machie type B. There are 16 hours/day available on machine typeA and 30 hours /day on machine type B. Profits gained by manufacturer from chair and table are birr 2 and birr 10 respectively.

A what should be daily production of each of the two products?

B use graphical method of LPP to find the solution

the following problem graphically.

Player B

Player A 3 -3 4

-1 1 -3

———————

Solve using simplex method

Maximize z= 21x+15x

Subject to the constraints - x - 2x >_ - 6

a departmental store, one cashier is there to serve the customers. And the customer

pick up their needs by themselves.

The arrival rate is 9 customers for every 5 minutes and

the cashier can serve 10 customers in 5 minutes, Assuming Poison arrival rate and

Exponential distribution for service rate,

find

i)

Avetage number of customers in the sestem

id.) Average time a customer spends in the system.

ili) Average number of customers in the queue or average queue length.

iv.) Average time a customer waits before being

served.

Following table shows the various activities of a construction project along with their duration:

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

Duration 20 25 10 12 6 10

a. Draw the network diagram for the project.

b. Find the critical path.

Using any secondary research method,

find out at least five applications of operations research in various industries.