Operations Research Answers

b) The table below shows a transportation problem. Solve it using the Vogel approximation

method.

Destinations

Sources 1 2 3 4 Supply

A 2 2 12 21 80

B 4 3 13 7 60

C 5 12 1 6 60

Demand 50 60 30 40

c) State five objectives of inventory management.

d) The following table shows a pay-off matrix for a game. Use it to solve the game.

e) State four characteristics of 2-persons zero sum game.

f) A company’s ordering cost is sh 25 and the holding cost is 10% of average inventory.

Given that the total cost is shs. 750, find the demand.

g) State the two categories of inventory models.

Solve by simplex method. Max z = 2x1 -x2 +2x3, 2x1 +x2 < 10, x1 +2x2 -2x3 <20x1 +2x3 < 5, x1, x2, x3 > 0

The Hardrock Concrete Company has plants in three locations and is currently working on three major construction projects, each located at a different site. The shipping cost per truckload of concrete, daily plant capacities, and daily project requirements are provided in the accompanying table.

Formulate an initial feasible solution to Hardrock’s transportation problem using Vogel’s Approximation Method.

The following statement are tru or false? Give a short proof or a example your answer

The ptimal solution for the following LPPis z*30

Maxz= x1-x2+3x3

Subject to x1+x2+x3<=, 10

X1, x2, x3>=0

Two vitamins A and B are to be given as health supplements on daily basis to students. There are two products Alpha & Beta which contain vitamins A and B. One unit of Alpha contains 2g of A and 1g of B. One unit of Beta contains 1g of A and 2g of B. Daily requirements for A and B are atleast 10g each. Cost per unit of Alpha is Rs. 20 and of Beta is Rs. 30. Formulate as LPP to satisfy the requirements at minimum cost

Three custom officers check the luggage of the passengers of an airport. The passengers are found to arrive at an average rate of 30 per 8 hours a day. The amount of time a custom officer spends with the passenger is found to have an exponential distribution with mean service time 32 minutes. (5) (i) Find the probability that all the custom officers are idle. (ii) Find the expected number of passengers in the queues. (iii) Find the expected waiting time of passenger in the system

1. A firm manufactures two products; the net profit on product 1 is Rupees 3 per unit and Rupees 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. (solve with graphical method)

Solve the following job sequencing problem by giving an optimal sequence of jobs, and find the total elapsed time also. Note that M1, M2, M3, M4, M5, and M6 are machines, and A, B, C, D are jobs.

Jobs → A B C D

M1 20 19 13 22

M2 10 8 7 6

M3 9 11 10 5

M4 4 8 7 6

M5 12 10 9 10

M6 27 21 17 14