DCSN 200 Exam 2 Solution, Spring 2009

MULTIPLE CHOICES 1 c 2 a 3d 4 a 5 c 6 d 7 b 8 c 9 c 10 a 11e 12 c 13b 14a 15d QUESTIONS Question 1 a) The center of gravity is: (24, 26) b) For (26, 24) For (24, 27) Distances are Distances are 24.74 26.17 15.23 17.46 48.70 45.22 Total cost = 11913 Total cost = 12377 The best location is (26,24) Question 2 a) Normalized weights are 0.4, 0.25, 0.15, 0.2 Composite scores on a 100-point scale Aspen Barclay Chester 79.25 67.75 74.5 b) Location Chester should be chosen, because it has the highest composite score of all locations that have each score equal 40 or more. Aspen has higher composite score, but it's 3rd score is below 40, so it is not chosen. Question 3 a) (8 + 10 + 8)/3 = 26/3 = 8.67 b) (Use naive to begin.) Month Demand Forecast March 6 - April 8 6 May 10 6 + .20(8-6)=6.4 June 8 6.4 + 20(10-6.4)=7.12 7.12 + .20(8 - 7.12) =7.296 c) Month March April May June Demand 6 8 10 8 Naïve - 6 8 10 Error - +2 +2 –2 MAD 6/3 = 2.0 Question 4 a) YEAR 1YEAR 2YEAR 3 avg index Q1 1710 1820 1830 1786.67 0.893 Q2 960 910 1090 986.67 0.493 Q3 2720 2840 2900 2820 1.41 Q4 2430 2200 2590 2406.67 1.203 total 7820 7770 8410 avg: 2000 b) year (x) 1 2 3 sales (y) 7820 7770 8410 annual sales trend: y = 7410 + 295x c) for year x=4, sales y = 8590 year 4 average per quarter is 2147.5 Breakdown into quarters is: 1918, 1059, 3028, 2583 Question 5 a) The weight of At – 1 is: α b) The weight of At – 2 is: α(1- α) c) The weight of At – 3 is: α(1- α)2 d) The weight of At – n is: α(1- α)n-1 e) The exponentially smoothed forecast with α = 1 is equivalent to the naive approach. Question 6 Product Selling price P Variable cost V V/P 1- V/P Sales Percent of sales Weighted contrib BEPX A $60 $20 .333 .667 $60,000 .0845 .0564 842.05 B $200 $80 .400 .600 $400,000 .5634 .3380 1684.3 C $25 $15 .600 .400 $250,000 .3521 .1408 8420.93 $710,000 1.0000 0.5352 a) The dollar break-even point for this firm is $320,000 / .5352 = $597,907. This is a calculator-based result; Excel reports $597,895. b) To break even, the firm should sell: 842 units of A, 1684 units of B, and 8421 units of C.