1. Star Technologies in Mumbai manufactures three 10 types of X ray machines -General type), Special Purpose type) and Tailor made type). Three shades of colours are required for painting the machines; these are white, black and silver. For production of a G type, we require 2 liters white and 3 liters of silver, for S type, we require 3 liters of white, 2 liters of black and 2 liters of silver, for T type, we require 5 liters of black and 4 liters of silver. It is assumed that the company has a stock of 58 liters of white, 100 liters of black and 150 liters of silver paints. Revenue collected by selling of one machine of G type is RS 1,00,000. For a machine of S type it is RS 1,50,000 and for T type, it is RS 2,00,000. The manufacturing cost of each machine is RS 80,000, RS 1,15,000 and RS 1,55,000 respectively.

Formulate the LPP in order to maximize the profit gained from selling the machines considering the resources available.

Can transportation problem be solved using a Linear Programming approach Justify your answer with example.

Discuss the significance of EMV term used in Decision making.

Describe and discuss 2 examples of Assignment Model. Do not discuss conventional example Le. Assignment of Machine to worker.

How will you use Simulation method to solve inventory problems? Discuss specifically stock and consumption level of inventory in the answer.

3. Minimize Z 30a 40b 40c, Subject to constraints.

a+4b+2c

5a+b+2c =180

a +3b +2c



Use simplex method to solve the above problem.

4. A firm has three Engineers, each engineer can work up to 185 hours during the next month, during this time, three projects must be completed. Three Projects need 120 hours, 140 hours and 180 hours respectively for completion. The amount (in RS) per hour that can be billed to the customer is as follows.

Project 1 2 3
Engineer 1 RS 1200 RS 1500 RS 1900
Engineer 2 RS 1400 RS 1300 RS 1200
Engineer 3 RS 1600 RS 1400 RS 1500

Formulate this as a Transportation problem 10 and allocate the number of hours with respect to the project for each Engineer.(State the assumptions made).

Also find the maximumoptimal total billings during the next month.

5. Assign the following jobs to operators C and D so that the total cost of operation is minimum. The costs in I.N.R. are given in the respective cells.

Operators
Jobs A B C D
1 40 20 20 70
2 80 90 20 60
3 60 50 50 70
4 50 70 90 60

A toy shop in Kolhapur has following daily demand pattern for a particular toy for a week along with associated probabilities as given below:

DAILY DEMAND 0 6 7 8 9 10
PROBABILITY 0.10 0.20 0.15 0.50 0.03 0.02

Use the following sequence of random numbers:

Random Numbers 21 38 60 16 12 05 73 19 10 49

Simulate the demand for next 10 8 weeks.

Also find out the average demand per 2 day.

The numbers of customer who arrive in a 4 Hotel Le Meridian appear to be Poisson distributed with a mean of 15 customers per day. The receptionist attends the customer at an average rate of 18 customers per day. Find the number of working hours for the receptionist in a day.

7. Use uncertainty criterions to decide the stock level for the demand pattern of 20, 30, 40 and 45 Kg Parle biscuits at a dealer. The buying price and selling price of the dealer for the biscuits being RS 30 and RS 40 per Kg. (Hint: You have to decide whether to maintain stock of 20,30,40 or 45 Kg).

State your decision under each uncertainty criteria. Use Alfa 0.7.

8. A company processes 5 jobs t which can be processed in the machines Band C. The processing time in minutes is given below.

What should be the sequence of the job to have minimum idle time?

Also calculate total elapsed time.

Jobs p q r s t

A 6 3 7 7 7

B 2 2 4 3 5

C 4 5 7 2 4