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Answers: COMM5005 Final Exam November 2009 Part A Q1 (e) Q2 (b) Q3 (d) Q4 (a) Q5 (b) Q6 (b) Q7( c) Q8 (d) Q9 (c) Q10 (b) Q11 (d) Q12(c) Q13 (a) Q14 (b) Q15 (e) Q16 (b) Q17 (c) Q18 (e) Q19 (c) Q20 (c) Part B Problem 1 (i) Profit=300x+200y Subject to 2 80 50 2 80 , 0 x y x y x y x y + + + (ii) (iii) Maximum at x = 30 y = 20 where Profit = 13,000 (iv) Profit=180x+80y Maximum at x = 40 y = 0 where Profit = 7200 Problem 2 (a)H 0 : π =0.056 H 1 : π >0.056 Check n π =9.52 >5 and n(1- π )=160.48>5 Test statistic Z=0.4934, Critical value Z 0.05 =1.645 Do not reject at the 5% level. We cannot conclude that the rate of defects is higher than usual. (b) Expected cost per cup = 72c (c) (62.31, 69.09) We can say with 99% confidence that the mean number of orders received per weekday lies between 62.31 and 69.09 Problem 3 (a) 1 2 3 4 ˆ 1.7736 0.6543 0.1533 0.1658 4.9953 Y X X X X = + +

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The number of bottles of white wine consumed at a wedding reception increases by 0.6543 for each extra guest, decreases by 0.1533 for each extra bottle of red wine consumed, decreases by 0.1658 for each extra litre of non-alcoholic drink consumed and increases by 4.9953 if transport is
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