Get premium membership and access revision papers, questions with answers as well as video lessons.
Got a question or eager to learn? Discover limitless learning on WhatsApp now -
Start Now!
Bms 100: Management Mathematics I August 2015 Question Paper
Bms 100: Management Mathematics I August 2015
Course:Bachelor Of Commerce
Institution: Kenyatta University question papers
Exam Year:2015
KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2014/2015
MAY SEMESTER EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
BMS 100: MANAGEMENT MATHEMATICS I
DATE: August 2015 TIME: 2 hours
INSTRUCTIONS:
Answer question ONE and any other TWO questions
QUESTION ONE (30 MARKS)
(a) Explain the following terms as used in set theory
(i) Finite set
(1 marks)
(ii) Disjoint sets
(1 marks)
(iii) Universal set
(1 marks)
(iv) Power set
(1 marks)
(b) Given that A = {e,f,g,h,k,m} and B = {e,h,i,n} and C = {g,h,i,l}
Determine the composition of the following set relations
i) A – B
(2 marks)
ii) A – (B$\bigcap$C)
(2 marks)
iii) n{A$\bigcup$B$\bigcup$C}
(c) Find the sum of the first 20 terms of the G.S $\frac14,\frac{7}{12}, \frac{11}{12},......$
(4 marks)
(d) The total cost C(Q) and total revenue R(Q) functions for a particular product are
C(Q) = 5,000,000 – 250Q + 0.002Q2
R(Q) = 1,250Q – 0.005Q2 where Q is the quantity produced and sold.
Determine:
(i) The profit maximizing level of output
(3 marks)
(ii) The maximum profit
(2 marks)
(iii) The output level at which total cost is minimum
(4 marks)
(e) A theater charges sh. 80 for each adult admission and sh. 50 for each child. One Sunday, 525 tickets were sold bringing a total of sh. 32, 550. How many of each type ticket were sold?
(3 marks)
(f) (i) Find the future value at the end of nine (9) years if an investment of sh. 15000 is deposited at the beginning of each year and the interest rate is 7.2% per annum compounded monthly.
(2 marks)
(ii) Recalculate the future value of the investment in (i) above taking the deposit at the end of each year instead.
(2 marks)
QUESTION TWO (20 MARKS)
(a) Explain the difference between the following terms as used in financial mathematics
(i) An annuity and a perpetuity
(2 marks)
(ii) Compounding and discounting
(2 marks)
(b) The total cost of producing a high technology product is given by
C = 3600 + 100q + 2q2. Suppose further that the weekly demand function for this product is p = 500 – 2q where p is the price per item and q is the number of units produced and sold. Find the number of units that will give the break even point for the product.
(4 marks)
(c) A business man seeks to borrow Ksh.70,000 from bank at a cost of 5% p.a The amount will be used to invest in any of two mutually exclusive project X and Y whose estimated cash flows are as follows: project X will yield uniform cash flows of Ksh. 20, 000 per year for four years. Project Y cash flows are Ksh.30,000 in the year 1, Ksh.22,000 in the year 2, Ksh. 18,000 in year 3 and Ksh.15,000 in the fourth year. Advice the business man on which project to invest in on the basis of
(i) Profitability Index
(6 marks)
(ii) Simple payback period
(6 marks)
Question three (20 marks)
(a) Explain the application of calculus in solution to problems in business
(3 marks)
(b) Evaluate the following definite integral $\int^3_1(3+5x)^5dx$
(3 marks)
(c) The joint total cost function for two products x and y is given as
C = f(x, y) = 50 + x2 + 8xy + y3
Find
(i) Partial derivative of C with respect to x
(2 marks)
(ii) Partial derivative of C with respect to y
(2 marks)
(iii) The level to which total cost will increase for each unit increase in product x given that 5 units of product x and 3 units of product y are produced.
(3 marks)
(d) A firm has analyzed its operating conditions and has developed the following functions
Total Revenue = - 10q2 + 200q
Total Cost = q2 – 20q + 1000
Where q is the number of units produced and sold.
Determine the value of q that:-
(i) Maximizes revenue and hence the maximum revenue
(4 marks)
(ii) Minimizes Total cost and hence the minimum total cost
(4 marks)
Question four (20 marks)
(a) A machine is valued at Ksh.100,000 on 1st January 2009. If depreciation at the end of each year is 20% of its value at the beginning of the year, find its value at the end of 8 years (apply sequences and series). (3 marks)
(b) A survey was conducted involving university students in hospitality management department. It was found that 40% study French ,50% study German, 30% study Russian, 20% study both French and German ,15% study both Russian and French ,
10% study both German and Russian, and 4% study all the three languages. The total number of students who did not study any of the three languages were 55. Find the number of students:
(i) Who were actually involved in the survey
(ii) Studying exactly one language
(4 marks)
(b) The monthly sales of a particular TV set is expected to decline at a rate of dS/dt=-25t2/5 TV set per monthly where t is time in months and S (t) is the number of TV sets sold each month. The company plans to stop manufacturing these TV sets when monthly sales reach 800 TVs. If currently at t = 0 the sales are 2000 TV sets, find
(i) The function S(t)
(3 marks)
(ii) How long the company will continue to manufacture these TV sets.
(2 marks)
(d) A company manufactures T – shirts and sells them for sh.54.90 each. The total cost function is linear and costs amount to Sh. 50,000 for 2000 T–shirts and Sh.32,120 for 800 T-shirts. Let x be the number of T–shirt sold.
(i) Write down the equation for total revenue
(2 marks)
(ii) Write the equation for total cost
(4 marks)
(iii) Find the break even quantity
(2 marks)
More Question Papers
Popular Exams
Return to Question Papers