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Business Mathematics I Question Paper
Business Mathematics I
Course:Bachelor Of Business Information Technology
Institution: Strathmore University question papers
Exam Year:2008
1
STRATHMORE UNIVERSITY
FACULTY OF INFORMATION TECHNOLOGY
Bachelor of Business Information Technology
SUPPLEMENTARY/SPECIAL SEMESTER EXAMINATION
MAT: MANAGEMENT MATHEMATICS (EVENING COURSE)
DATE: August 2008 TIME: 2 Hours
ATTEMPT QUESTION ONE AND ANY OTHER TWO QUESTIONS
Question 1 (30 marks)
(a) What do you understand by the following terms?
(i) Discrete Process
(ii) Markov Chain
(iii) Sensitivity Analysis
(iv) State matrix
(v) Feasible solution
(vi) Input output model
(6 marks)
(b) In small town, 60% of all sunny days are followed by sunny days and 80% of all cloudy
days are followed by cloudy days. Construct transition diagram for this and give the
transition matrix.
(6 marks)
(c) Anita wants to use milk and orange juice to increase the amount of calcium and
vitamin A in her daily diet. An ounce of milk contains 38milligrams of calcium and
56micrograms of vitamin A. An ounce of orange juice contains 5milligrams of
calcium and 60micrograms of vitamin A. Determine how many ounces of milk and
orange juice Anita should drink each day to provide exactly 550milligrams of
calcium and 1200micrograms of vitamin A by crammers rule.
(6 marks)
(d) A firm manufactures two products, each of which must be processed through
departments X and Y. The table below summarizes labor- hour requirements per
unit for each product in each department. Also presented are weekly labor- hour
capacities in each department and respective profit margins for the two products.
Determine the number of units to produce of each product so as to maximize total
contribution to fixed cost and profit.
Product A Product B Weekly labor capacity
Department X 3hr per unit 2hr per unit 120 hours
Department Y 4hr per unit 6hr per unit 260 hours
Profit margin $5 $6
(8 marks)
2
(e) Determine the dual for the following
Minimize Z = 60x1 + 30x2
(4 marks)
Question 2 (20 marks)
(a) Suppose a farmer has 50 ha of land and wishes to plant maize and beans and possibly
leave some land to recover. The farmer has a maximum of $27,000 to use for cultivation and a maximum labour capacity of 160 human days. The following information is availed on the
profit and labour charges per ha of land.
Resource/Crop Maize Beans
Cultivation $300 $600
Labour 4 people 2 people
Expected profit per ha $300 $400
(i.) Formulate a linear programming model based on the above information given that the
farmer wants to maximize profit and assuming that there will be no drought.
(ii.) Solve the problem and advise the farmer on how to utilize his land so as to maximize his
profit.
(10 marks)
(b) Suppose the entire cola industry produces only two colas. Given that a person last
purchased cola 1, there is a 90% chance that her next purchase will be cola 1. Given that
a person purchased cola 2, there is an 80% chance that her next purchase will be cola 2.
(i.) If a person is currently a cola 2 purchaser, what is the probability that she will
purchase cola 1 two purchases from now?
(ii.) If a person is currently a cola 1 purchaser, what is the probability that she will
purchase cola 1 three purchases from now?
(iii.) Construct a transition diagram for the above process.
(10 marks)
Question 3 (20 marks)
Define what you understand by, Surplus variables, and Artificial variables and hence
solve the following LP problem
1 2 3
1 2 3
1 2 3
1 2 3
Maximize, 2 3 5
Question 4 (20 marks)
An economy is based on 3 industries coffee, energy and transportation. Production of a
dollar’s worth of coffee requires an input of $ 0.10 from coffee industry, and $ 0.60 from
energy industry. Production of a dollar’s worth of energy requires $ 0.10 from energy
industry, and $ 0.70 from the transportation industry. Production of a dollar’s worth of
transportation requires $ 0.40 from coffee industry, $ 0.20 from the energy industry and $
0.20 from the transportation industry.
(i.) Define and find the technology matrix, A
(ii.) Find (I-A)-1
(iii.) the output from each industry that is required to satisfy a final demand of
$10 million for A, $10 million for B and $10 million for C
(iv.) What are the assumptions that you made in solving the above?
Question 5 (20 marks)
(a) What do you understand by
(i.) Imbalanced Transportation model
(ii.) Network
(iii.) Directed Graph
(b) Given the data for a transportation problem below, formulate the mathematical
model which minimizes the total cost.
Destination
Origin 1 2 3 Supply
1 20 30 10 100
2 30 40 25 300
3 35 15 20 100
Demand 150 125 225
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