SCHOOL OF ACCOUNTING AND BUSINESS. BSc. (APPLIED ACCOUNTING) GENERAL / SPECIAL DEGREE PROGRAMME. YEAR I SEMESTER I (Group A)

Transcription

1 All Rights Reserved No. of ages - 04 No of Questions - 08 SCHOOL OF ACCOUNTING AND BUSINESS BSc. (ALIED ACCOUNTING) GENERAL / SECIAL DEGREE ROGRAMME YEAR I SEMESTER I (Group A) END SEMESTER EXAMINATION FEBRUARY 015 QMT Business Mathematics Date : 06 th Februar 015 Time : 9.00 a.m p.m. 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. Ranjan wants to have a total of Rs in two ears so that he can put a hot tub on his deck. He finds an account that pas 5% annual interest compounded monthl. How much should Ranjan invest in this account so that he ll have Rs at the end of two ears? ii. Suppose Ranjan, from our part (i), onl has Rs to invest but still wants Rs for a hot tub. He finds a bank offering 5.5% annual interest compounded quarterl. How long will he have to leave his mone in the account to have Rs ? iii. You have a choice from the following mutuall exclusive investments. If ou require a 15% return,which investment should ou choose? Cash Flow Year roject A roject B 0 (100000) (15000) Question No. 0 A bank gives a mortgage of 450,000 dollars for 30 ears with 6% annual interest. What would be the the monthl repament figure of a person who takes the mortgage? After 10 ears, if the interest rate increases to 8% per annum what would be the new monthl repament figure? Hint: ODI = R { 1 (1+r) n r } A ODI = R { (1+r)n 1 } r 1

3 Question No. 03 The demand and suppl functions under perfect competition are given b p d = 00 q and p s = 3q + 56 respectivel. Where p and q are the price and the quantit. i. Find the equilibrium quantit and the equilibrium price. ii. Sketch the demand and the suppl functions clearl stating all the required points. iii. Highlight the consumer and producer surpluses and indicate in the sketch. iv. Find the consumers surplus. v. Find the producers surplus. Hint: x n dx = xn+1 n+1 + C Question No. 04 i. Considering the following summer of the Cash flows, find the NV for the following project if the current rate is 10.5% Time Cash flow ($) 0 (300) ii. A printing machine is to be replaced in 7 ears,. A new machine is expected to cost Rs Assuming an annual interest rate of 6 %, what will be the size of each annual savings in order to bu the new printing machine?

4 Question No. 05 i. The profit function(x, ) = 360x x 36x of a firm is assumed to have a monopol on x and, but the markets do not intersect a. Find the two first order partial derivatives b. Set and x and x equal to zero and solve for x and. c. Find the second order partial Derivatives x x, and. x. d. Evaluate the second order partial derivatives at the critical points obtained in part (b). e. Show that the following condition holds at the critical point x x x f. Since the above condition is satisfied, the critical point is an extremum point for the profit. Find the extremum profit? Question No. 06 i. rove that the marginal cost MC must be equal to the marginal revenue MR at the profit maximizing level of output. ii. Total revenue and the total cost functions of a firm are R 8400Q 36Q and C Q respectivel. a. Set up the profit function. b. Find the critical value/s where is at a relative extremum and test the second order condition. c. Calculate the maximum profit. 3

5 Question No i. If A and B Find the matrix X which satisfies the following relationship 5A B 4X 0 ii. Ms. Sona. invested Rs. 30,000; part at 5%, and part at 8%. The total interest on the investment was Rs.,100. Transform this word problem in to a sstem of simultaneous equations and solve the problem using a matrix method Question No. 08 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 ii. A compan has two factories that produce T.V. sets. The two factories are located at A and B. The number of units of T.V. sets produced per month b the factor located at A is x while the number of units of T.V. sets produced per month b the factor located at B is. The joint cost function for the production of T.V. sets per month is given b C(x, ) = 6x + 1 The compan has a demand of 90 units of T.V. sets per month. Find the number of units of T.V. sets that should be produced per month b each factor to minimize the cost of production per month and find the optimal cost. 4