Essay about Econ1202 Semester 2 2008 Final Exam

1301 Words May 2nd, 2013 6 Pages
THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF ECONOMICS ECON1202/2291 QUANTITATIVE MEHODS A FINAL EXAMINATION SESSION 2 2008
TIME ALLOWED - 3 HOURS

THIS PAPER IS WORTH 60% OF THE TOTAL SUBJECT MARK
Questions: 7 Students must attempt no more than 6 questions Marks per question: 10 Exam weighting: 60%.

Instructions to Students:

- Complete all of the details required on the front page of the examination booklet. - Make sure that you note the SIX(6) questions attempted on the front of your examination booklet - If Seven questions are attempted, the first SIX(6) will be marked. - You may use a non-programmable calculator - Graph paper will be provided. - Answers are to be written in ink. Pencils are permitted for graphing purposes. - The
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(3 marks) c) Determine the optimal number of bus and train travelers. (2 marks) d) Say a train strike significantly reduced the number of trains available. By how much would the train capacity constraint have to fall for the optimal solution to be altered? (2 marks)

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Question 5:
a) Consider the implicit function 2x4 (y − 1) + exy = 7 Find the rate of change of y with respect to x when x = 2, y = 1. (2 marks) b) Find: 12y + 6 dy +y+3

y2 (3 marks)

c) In the small town of Lametopia, which has a population of 80,000 people, the town council (of 100 people) hears in advance that the town might have won “Tidiest city 2008.” News circulates about the town quickly, such that by the end of the first week (one week after the council heard the news!) 1000 people know the rumour. Assuming growth is logistic, find how many individuals should have heard the rumour after two weeks. (5 marks)

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Question 6:
a) An importer of antiquities knows that he can sell bowls and carved figurines to the domestic market. If q1 is this number of figurines sold, their price will be $(60 − 2q1 ). If q2 bowls are sold, $(10 − q2 ) will be the price of bowls. Figurines cost $16 and bowls $4 to the importer and fixed costs are $200. i) How many each of figures and bowls should be sold to maximise profit. ii) Is this indeed a maximum? Justify using second order conditions. iii) What price is

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