SCHOOL OF ACCOUNTING AND BUSINESS BSc. (APPLIED ACCOUNTING) GENERAL / SPECIAL DEGREE PROGRAMME 2014/15

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1 All Rights Reserved No of ages - 05 No of Questions - 07 SCHOOL OF ACCOUNTING AND BUSINESS BSc (ALIED ACCOUNTING) GENERAL / SECIAL DEGREE ROGRAMME 014/15 YEAR I SEMESTER I (Group A) END SEMESTER EXAMINATION JUNE 014 QMT Business Mathematics Date : 30 th June 014 Time : 900 am pm Duration : Three (03) Hours Instructions to Candidates: Answer an five (05) questions The total marks for the paper is 100 All questions carr equal marks Use of scientific calculator is allowed Formula Sheet is provided Answers should be written neatl and legibl

2 Question No 01 i Show that the marginal cost [MC] must be equal to the marginal revenue [MR] at the profit maximizing level of output Total Revenue [TR] and the Total Cost [TC] functions of a firm are TR 8400Q 36Q and TC Q respectivel a Set up the profit function b Find the critical value/s where is at a relative extremum c Use the second order condition to distinguish the critical point/s d Calculate the maximum profit (Total 0 Marks) Question No 0 The profit function x, 360x 04 4x36x have a monopol on x and of a firm is assumed to i Find the two first order partial derivatives and x i Set and x equal to zero and solve for x and Find the second order partial Derivatives x x, and x iv Evaluate the second order partial derivatives at the critical points obtained in part (ii) v Show that the following condition holds at the critical point x x x vi Since the above condition is satisfied, the critical point is an extremum point for the profit Find the extremum profit? (Total 0 Marks) 1

3 Question No 03 i If U(x,, z) = 3x z + 4x z + 5 4, without using Euler s theorem prove that x U U U + + z x z = 4U Let U(x,) be a multivariable function in x and U is said to be homogeneous function of order n if U(x) = n U(x,) 5 5 x If U ( x, ) show that U(x,) is a homogeneous function of degree three x i A compan has two factories that produce TV sets The two factories are located at A and B The number of units of TV sets produced per month b the factor located at A is x while the number of units of TV sets produced per month b the factor located at B is The joint cost function for the production of TV sets per month is given b C(x, ) = 6x + 1 If the compan has a demand of 90 units of TV sets per month Find the number of units of TV sets that should be produced per month b each factor to minimize the cost of production per month and find the optimal cost (Total 0 Marks) Question No i If A and B Find the matrix X which satisfies the following relationship 3A B 4X 0 ii Two tpes of radio valves A, B are available for assembling two tpes of radios and Q in a small factor The factor uses valves of tpe A and 3 valves of tpe B for a tpe of radio, and for a tpe of radio Q it uses 3 valves of tpe A and 4 valves of tpe

4 B The number of valves of tpe A and B used b the factories are 130 and 180 respectivel a Identif the unknowns to be evaluated in the above problem b Develop the sstem of simultaneous equations which represent the above problem c Find the number of radios assembled through the solution of the sstem of simultaneous equation ou developed in part (b) using the matrix method (Total 0 Marks) Question No 05 d MR TR Q Q dq i Marginal revenue of a firm is given b a Find the Total revenue function b Find the number of items to be sold to maximize the revenue c Find the maximum revenue The rate of net investment is I 10 t 1/ 5 and capital stock at t 0 is 150 If the relationship between capital function K and the net investment is given b K I dt Find the capital function K, using the given boundar condition att 0, K 150 i a Using our knowledge on partial fractions show that x 1 4 1/ x 4 1/ 4 x b Hence or otherwise find 1 dx x 1 (Total 0 Marks) 3

5 Question No 06 i A sum of was deposited in a bank at an interest rate of 13% compounded quarterl Seven ears later the rate decreased to 7% compounded semiannuall If the mone was not withdrawn, how much was in the account at the end of 10 ears after the deposit was made? Over 5 ears a bond costing $ 000 increases in value to $ 700 Find the effective annual rate i A machine depreciates b 0 percent in the first ear, then b 10 per cent per annum for the next 5 ears and b per cent per annum thereafter Find its value after 7 ears if its initial price is 70,000 iv A compan purchase a machine $ 1,000 The machine Contribute $ 3,500 per annum for five ears After 5 ears it is scrapped for $ 1000 Find the Net resent Value of the machine if the interest is 5% per annum (Total 0 Marks) Question No 07 i A Manager expects the following cash flow pattern in a new project that the plan to launch The manager needs our help to find the internal rate of return of the project Time Cash flow ($ 000) 0 (80)

6 A $ mortgage is taken out on a propert at a rate of 10 percent for 30 ears a What will the monthl repament be? b After 15 ears of the mortgage, the interest rate increases to 13 percent, b what amount the monthl repament figure increase (Total 0 Marks) FORMULA SHEET QMT V = (1 + r n) V = (1 + r) n V = (1 r) n 1 (1 + r) n ODI = R { } A r ODI = R { (1 + r)n 1 } r ER = R { 1 r } NV 1 IRR = r 1 + { } (r NV 1 NV r 1 ) A 1 = ( 1 A ) adj(a) AX = b X = A 1 b 5