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Management Maths Ii(B) Question Paper

Management Maths Ii(B)

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2010

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATION 2009/2010
FIST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF COMMERCE
BMS 102:MANAGEMENT MATHS II (B)
DATE:Tuesday 9th February 2010 TIME:11.00 AM-1.00 PM
INSTRUCTIONS
Answer question one(compulsory)and any other TWO questions.
Question one:(30 marks)

a)A portfolio manager is considering 30 stocks for investment.only 15 stocks will be selected for inclusion in a portfolio.How many different combinations of stocks can be considered?(3 marks)
b)use crammers rule to solve the system of equations.(7 marks)
2x+4y+6z=18
4x+5y+6z=24
3x+y-2z=4
c)Explain the following terms as used in decision theory(4 marks)
i)action space
ii)pay off table
iii)state of the nature
iv)opportunity loss
d)A factory manufacturing nails has 3 machines A1,A2,A3 in operation.Machine A1 produces 50% of the nails and is known to have a rate of 3% defective.Machine A2produces 30% of the nails with the rate of 4% defective,and machine A3 produces 20% with rate of 5%defective.
i)A nail is selected at random from the nails produced by the factory,what is the probability that it will be defective?(3 marks)
ii)A nail selected at random from this factory was found to be defective,find the probability that this nail was produced by machine A1.(2 MARKS)

e)In a recent survey on the use of bathing soaps,the findings was as follows;
Out of those who used Lux at last purchase,10% switched to Geisha,10% switched to Imperial and 10% to Dove.Out of those who use Geisha,20%switched to Imperial and 10% to Dove.Out of those who used Imperial only 10% switched to Dove.Out of those who used dove,205 switched toLux,10% to Geisha and 10% to Imperial.
i)construct the consumer brand switching matrix (2mks)
ii)Determine the expected market share of each soap in the next period.(2 mks)
iii)Comparing the initial market share with the current share,which brand have favourable brand switching patterns?(1mk)

f)A company stocks an item that is consumed at the rate of 50 units per day.It cost he company $20 each time an order is placed.An invetory unit held in stock for a week will cost $35.
i)Determine the optimum inventory policy,assuming a lead time of one week.(3mks)
ii)Determine the optimum number of orders per year(based on 365 days per year)

QUESTION 2:(20 MKS)
a)Consider the following problem with three decision alternatives and three state of nature with following pay off table reprenting profit.
Decision state nature
S1 S2 S3
D1 4000 4000 -2000
D2 0 3000 -1000
D3 1000 5000 -3000
i)What is the optimal decision if the decision maker were consevertive.(2mks)
ii)What is the optimal decisin if the decision maker were optimistic?(2mks)
iii)What is the optimal decision using minimax regret approach?(2 MKS)
IV)Given that P(S1)=0.20,P(S2)=0.50,P(S3)=0.30, calculate the expected value of perfect information.(3 mks0
v)
a)briefly explain four types of costs associated with stock.(4mks)
b)solve the following system of equations using the matrix method approach.(7 mks)
2x+4y+6z=18
4x+5y+6z=24
3x+y-4z=4
QUESTION 3:(15 MKS)
a)A company produces three products P,Q and R from three raw materials A,B and L.One unit of prduct P requires 1 unit of A,3 units of B and 2 units of L.One unit of Q requires 2 units of A and B each,and 3 units of L.One unit of R requires 2 units of A,6 units of B and 4 units of L.The compay has a daily availabiliy of 8 units for A,12 units for B and 12 units for L.It is further known that the unit contribution margin for the products is sh.3,2 and 5 respectively for P.Q and R.Formulate the problem as a linear programming problem and then solve it to determine the optimun product level.(15mks)

Management Maths Ii(B) Question Paper

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