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Bms 102: Management Mathematics Question Paper
Bms 102: Management Mathematics
Course:Bachelor Of Commerce
Institution: Kenyatta University question papers
Exam Year:2014
INSTRUCTIONS: ANSWER QUESTION ONE AND ANY OTHER TWO
QUESTION ONE (30 MARKS)
a) The matrix of technical coefficients of inputs in coal and iron industries is as follows;
Coal Iron
Coal 0.2 0.2
Iron 0.6 0.2
If the final demands of coal and iron are sh 240 million and sh 80 million, calculate the output for each industry (5 marks)
b) Three machines are used a part for a product. It has been observed that 60 percent of the parts are made on machine A, 25 percent on machine B and 15 percent on machine C. Machines A,B and C produce 90 percent, 95 percent and 92 percent non-defectives respectively. If a part is picked at random is found to be defective, then:
i. What is the probability that it has been made on machine A? (2 marks)
ii. What is the probability that it has been made on machine B? (2 marks)
iii. What is the probability that it has been made on machine C? (2 marks)
c) Briefly explain the different decision rules usually adopted in the context of decision making under uncertainty (10 marks)
d) Define the term inventory management (2 marks)
e) A furniture firm produces chairs, tables and cupboards, each requiring three types of raw materials: timber, nails and varnish. Given below are the requirements of different raw materials for producing one unit of each product:
Product Timber (cft) Nails (g) Varnish (litres)
Chair 0.8 20 1
Table 1 40 1.5
Cupboard 3 60 2
If the firm produces 300 chairs, 100 tables and 75 cupboards, find the quantity of each raw material using matrix algebra. (6 marks)
QUESTION TWO (20 marks)
a) Briefly discuss any FOUR assumptions of linear programming (8 marks)
b) A company produces two types of pen; fancy and pointy. Profits on fancy pen and pointy pen are sh 5and sh 3 respectively. Raw material required for each fancy pen is twice of that required for pointy pen. The supply of raw material is sufficient enough only for 1000 pointy pens per day. Biro pen requires a special clip and only 400 clips are available per day.
i. Formulate the above as a Linear programming model (3 marks)
ii. Determine the number of each type of pens the company the company should produce in order to maximize profits. (9 marks)
QUESTION THREE (20 marks)
a) A company follows an EOQ system for its inventory. The annual demand for one of the components it uses is 24000 units. The cost of the component is sh 80 per unit and the cost per order is sh 400.The company estimates the carrying costs to be 24 percent.
i. Determine the economic order quantity for the component (3 marks)
ii. How many orders should the company place per year (2 marks)
iii. Determine the total annual inventory cost (3 marks)
iv. If the company decides to place an order every month, what will be the effect of this ordering policy? (4marks)
b) A manufacturing company is bringing out a new product. The company has to decide whether to bring out a full, partial or a minimum product line. The company foresees three levels of product acceptance and has estimated their payoffs as given in the table below:
Product acceptance Probability Product line
Full Partial Minimum
Good 0.2 80 70 50
Fair 0.4 50 45 40
Poor 0.4 -25 -10 0
Advise the company on which product line to bring out using the;
i. Expected value criterion (3 marks)
ii. Expected opportunity loss criterion (5 marks)
QUESTION FOUR (20 marks)
a) New razor blades were introduced in the market by three companies at the same time. When they were introduced each company had an equal market share but during the first year the following changes took place : company A retained 90 percent of its customers ,lost 3 percent to B and 7 percent to C. Company B retained 70 percent of its customers, lost 10 percent to A and 20 percent to C. Company C retained 80 percent of its customers, lost 10 percent to A and 10 percent to B. Assuming that no changes in the buying habits of customers occur, determine the following;
i. The transition probability matrix and the initial conditions vector (2 marks)
ii. The market shares of the three companies at the end of the second year (3 marks)
iii. What are the long run market shares of the three companies (5 marks)
b) An elementary school is offering 3 language classes; one in Spanish, one in French, and one in German. These classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 in the French class and 16 in the German class. There are 12 students that are in both Spanish and French, 4 in both Spanish and German, 6 in both French and German, and 2 taking all three.
i. If a student is chosen randomly, what is the probability that he or she is not in any of these classes? (2 marks)
ii. If a student is chosen randomly, what is the probability that he or she is taking exactly one language course? (3 marks)
iii. If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class? (5 marks)
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