8/6/2019 BSCS2011 M Operations Research Assignment 1

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UNIVERSITY OF KARACHIDEPARTMENT OF COMPUTER SCIENCE

(MORNING PROGRAMME)

BACHELOR OF SCIENCE IN COMPUTER SCIENCESEMESTER FIRST SEMESTER 2011

COURSE BSCS-507 OPERATIONS RESEARCH I

ASSIGNMENT I

SUBMISSION DUE DATE : 3RD FEBRUARY 2011

Q. During the class session held on Thursday 27th

January 2011, we discussed the problemrelated to the model known as Blending Problem Modelin the field of Operations

Research.

Many computations that commonly occur in Operations Research and its various

branches including Linear Programming, and many other branches ofMathematics canbe concisely expressed in the form ofsystem of linear equations and hence can be solved

by usingmatrices. This assignment question is based on the same scenario.

Suppose an oil company manufactures two types ofpetroleumproducts, that is, regularpetroland supreme petrol. These products are produced by mixing togethertwo types of

crudeoils, that is,crude oil #1 andcrude oil #2, in an appropriate ratio. The quantity ofeach type ofcrude oilrequired to manufacture 1 litre of each type ofpetroleum product is

given as:

For 1 litre Regular petrol: 0.30 litre Crude oil #1 & 0.70 litre Crude oil #2

For 1 litre Supreme petrol: 0.40 litre Crude oil #1 & 0.60 litre Crude oil #2

From this information we can find the quantity of each type of crude oilneeded tomanufacture a given quantity of thepetroleum products.

How would you use the notion ofmatrices to mathematically express these relationships;

and how would you solve the problem of determining the quantity of each type ofcrudeoilrequired in order to be able to produce some given quantities of the two petroleum

products?

Finally, design a table having four columns,Regular petrol, Supreme petrol, Crude oil #1

unusedand Crude oil #2 unused. Now fill the table with the values to show how muchRegular petroland Supremepetrolcan be produced with the given quantity of Crude oil

#1 and Crude oil #2, and the how much of these ingredients will be left in each case.Assume that the given quantity of Crude oil #1 is 5 litres and of Crude oil #2 is 8 litres.

Your table may have infinite rows (why!?!?); you are required to show only few rows in

the table as discussed during the class session.

IMPORTANT INSTRUCTIONS:

Remember, the assignments may help you for the preparation of your future quizzesand/or examinations!

All the assignments must be submitted HAND-WRITTEN on A-4 size paper(s). Sobe careful, if you dont know what is A-4 size , your marks are liable to deduction!

WISH YOU THE BEST OF LUCK*******************************