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NORTH·WEST UNIVERSITY
YUNIBESITI YA BOKONE·BOPHIRIMA
NOORDWES· UNIVERSITEIT
MAFIKENG CAMPUS
EXAMINATION OFFICE
EXAMINATION 1st OPPORTUNITY NOVEMBER 2011
FACULTY COMMERCE AND ADMINISTRATION
DEPARTMENT STATISTICS AND OPERATIONS RESEARCH
COURSE TITLE INTRODUCTION TO OPERATIONS RESEARCH
COURSE CODE STOM 228
TIME 3 HOURS
MARKS 100
1ST EXAMINER MR. L.D XABA
2ND EXAMINER MR. N. N MARUMA
Instruction to Candidates
1. Answer ALL questions
2. Scientific calculators will be allowed
3. Look at how marks are allocated and plan your time and answer
4. Write logically, legibly and number your answer
CANDIDATES ARE NOT ALLOWED TO READ THE QUESTIONS UNTIL THEY ARE
TOLD TO DO SO BY THE CHIEF INVIGILATOR.
, Question 1 [14 Marks1
Use Gauss reduction method to solve the system of linear equation:
1.1. x 2y = 6 - 4z
x+13z=6 Y
-2x + 6y - z = - 10
Question 2[20 Marks]
Solve the following LP problem graphically:
2.1. A housewife wishes to feed her children a breakfast menu which contains a specified level
of nourishment. After consulting her dietician, she decides that her children should get at least
one milligram of thiamine, 5 mgs of niacin and 400 calories a day at breakfast. The children have
a choice of eating the latest cereals- Noisies, the old standby Crispies, or as children often prefer,
a mixture if the two. The small print on the side of each cereal box contains, apart from knitting
patterns and assorted recipes, the fact that one spoonful ofNoisies contains 0.1 mg of thiamine, 1
mg of niacin and 110 calories, while one spoonful of Crispies contains 0.25 mg of thiamine, 0.25
mg of niacin and 120 calories.
a. Formulate the nutrient constraints. (4)
b.IfNoisies cost 3.6 cents per spoonful and Crispies 4.2 cents per spoonful determine the
cheapest mixture ofNoisies and Crispies which satisfied the nutrient constraints. (8)
2.2. Outline eight (8) steps in solving an linear programming problem graphically. (8)
Question 3[30 marks]
Solve linear equation using simplex method:
1. Maximize z 2XI - 8X2
S.t
XI + 3X2:S 12
3xI + 2X2:S 18
(15)
2. Min w ::::: 2x + lOy + 8z
S.t X + Y + z~ 6
y+ 2z~ 8
-x + 2y + 2z ~ 18
x,y,z~O (15)
NORTH·WEST UNIVERSITY
YUNIBESITI YA BOKONE·BOPHIRIMA
NOORDWES· UNIVERSITEIT
MAFIKENG CAMPUS
EXAMINATION OFFICE
EXAMINATION 1st OPPORTUNITY NOVEMBER 2011
FACULTY COMMERCE AND ADMINISTRATION
DEPARTMENT STATISTICS AND OPERATIONS RESEARCH
COURSE TITLE INTRODUCTION TO OPERATIONS RESEARCH
COURSE CODE STOM 228
TIME 3 HOURS
MARKS 100
1ST EXAMINER MR. L.D XABA
2ND EXAMINER MR. N. N MARUMA
Instruction to Candidates
1. Answer ALL questions
2. Scientific calculators will be allowed
3. Look at how marks are allocated and plan your time and answer
4. Write logically, legibly and number your answer
CANDIDATES ARE NOT ALLOWED TO READ THE QUESTIONS UNTIL THEY ARE
TOLD TO DO SO BY THE CHIEF INVIGILATOR.
, Question 1 [14 Marks1
Use Gauss reduction method to solve the system of linear equation:
1.1. x 2y = 6 - 4z
x+13z=6 Y
-2x + 6y - z = - 10
Question 2[20 Marks]
Solve the following LP problem graphically:
2.1. A housewife wishes to feed her children a breakfast menu which contains a specified level
of nourishment. After consulting her dietician, she decides that her children should get at least
one milligram of thiamine, 5 mgs of niacin and 400 calories a day at breakfast. The children have
a choice of eating the latest cereals- Noisies, the old standby Crispies, or as children often prefer,
a mixture if the two. The small print on the side of each cereal box contains, apart from knitting
patterns and assorted recipes, the fact that one spoonful ofNoisies contains 0.1 mg of thiamine, 1
mg of niacin and 110 calories, while one spoonful of Crispies contains 0.25 mg of thiamine, 0.25
mg of niacin and 120 calories.
a. Formulate the nutrient constraints. (4)
b.IfNoisies cost 3.6 cents per spoonful and Crispies 4.2 cents per spoonful determine the
cheapest mixture ofNoisies and Crispies which satisfied the nutrient constraints. (8)
2.2. Outline eight (8) steps in solving an linear programming problem graphically. (8)
Question 3[30 marks]
Solve linear equation using simplex method:
1. Maximize z 2XI - 8X2
S.t
XI + 3X2:S 12
3xI + 2X2:S 18
(15)
2. Min w ::::: 2x + lOy + 8z
S.t X + Y + z~ 6
y+ 2z~ 8
-x + 2y + 2z ~ 18
x,y,z~O (15)
