UNIVERSITY OF THE COMMONWEALTH CARIBBEAN SCHOOL OF BUSINESS & MANAGEMENT FALL SEMESTER 2021 (Online) FINAL SEMESTER PRACTICE PAPERQUESTIONS & ANSWER KEY QUESTION 1 Given the following data on hotel check-ins for a 6-month period: Month July August September October November December # of Rooms 70 rooms 105 rooms 90 rooms 120 rooms 130 rooms 115 rooms A). What is the 3-month moving average forecast for January? (1 mark) Answer: 121.67 B). With alpha = 0.3, what is the simple exponential smoothing forecast for October? Assume the forecast for July was 75 rooms. (3 marks) Answer: Demand Forecast July 70 75 Aug 105 73.5 Sept 90 82.95 Oct 120 85.065 Nov 110 95.546 Dec 115 105.882 October forecast is 85.065 rooms C) Using a weighted moving average with weights of 0.6, 0.3, and 0.1 (from most recent), how many check-ins can be forecasted for January? (1 mark) Answer: 120 D) The last four weekly values of sales were 80, 100, 105, and 90 units, respectively. The last four forecasts (for the same four weeks) were 60, 80, 95, and 75 units, respectively. Calculate the MAD, MSE, and MAPE for these four weeks. 91 +2 +2 marks) Sales 80 100 105 90 Forecast 60 80 95 75 Error Error squared Pct. error Answer: MAD = 65/4 = 16.25; MSE = 1125/4 = 281.25; MAPE = 0.712/4 = .178 or 17.8% QUESTION 2 A network consists of the following list. Times are given in weeks. Activity Preceding Optimistic Probable Pessimistic A -- 5 11 14 B -- 3 3 9 C -- 6 10 14 D A, B 3 5 7 E B 4 6 11 F C 6 8 13 G D, E 2 4 6 H F 3 3 9 (a) Draw the network diagram. (3 marks) (b) Calculate the expected duration and variance of each activity. (3+2 marks) (c) Calculate the expected duration and variance of the critical path. (2 marks) Answer: (a) (b, c) Expected Task time Variance Std. dev. A 10.5 2.25 1.5 3 B 4 1 1 8 C 10 1.778 1.333 0 D 5 0.444 0.667 3 E 6.5 1.361 1.167 8 F 8.5 1.361 1.167 0 G 4 0.444 0.667 3 H 4 1 1 0 1 Project 22.5 Project 4.139 Std. dev. 2.034 (d) z = (28 - 22.5)/2.03 = 2.71, (P ≤ 28) = .997 Slack Variance 1.778 1.361 QUESTION 3 The sales manager of a large apartment rental complex feels the demand for apartments may be related to the number of newspaper ads placed during the previous month. She has collected the data shown in the accompanying table. Ads purchased, (X) Apartments leased, (Y) 15 6 9 4 40 16 20 6 25 13 25 9 15 10 35 16 a) Find the least squares regression equation. (5 marks) b) Estimate sale if the number of advertisements purchased is 30. (1 mark) c). Find the coefficient of determination (4 marks) soln: Ads, X (X – X )2 (X – X )(Y – Y ) 6 15 64 32 4 9 196 84 16 40 289 102 6 20 9 12 13 25 4 6 9 25 4 –2 10 15 64 0 16 35 144 72 Leases, Y Y = 80 X = 184 (X – X )2 = 774 (X – X )(Y – Y ) = 306 from : so b1 XY nXY X n( X ) 2 2 and b 0 = Y-b1 X Y 80 184 10; X 23 8 8 b1 = 306/774 = 0.395 b0 = 10 – 0.395(23) = 0.915 The estimated regression equation isŶ = 0.915 + 0.395X or Apartments leased = 0.915 + 0.395 ads placed b).If the number of ads is 30, we can estimate the number of apartments leased with the regression equation 0.915 + 0.395(30) = 12.76 or 13 apartments The coefficient of determination. SST = 150; SSE = 29.02; SSR = 120.76 Y X (Y– Ῡ)2 Yˆ = 0.915 + (Y – Yˆ )2 ( Yˆ –Ῡ)2 0.395X 6.00 15.00 16 6.84 0.706 9.986 4.00 9.00 36 4.47 0.221 30.581 16.00 40.00 36 16.715 0.511 45.091 6.00 20.00 16 8.815 7.924 1.404 13.00 25.00 9 10.79 4.884 0.624 9.00 25.00 1 10.79 3.204 0.624 10.00 15.00 0 6.84 9.986 9.986 16.00 35.00 36 14.74 1.588 22.468 80.00 184.00 SST=150.00 80.00 SSE=29.02 SSR=120.76 From this the coefficient of determination is r2 = SSR/SST = 120.76/150 = 0.81 QUESTION 4 A) Perform an ABC analysis on the following set of products.( 3maeks) Annual Item Demand Unit Cost A211 800 $9 B390 100 $90 C003 450 $6 D100 400 $100 E707 85 $2,000 F660 250 $320 G473 500 $75 H921 100 $75 Answer: The table below details the contribution of each of the eight products. Item E707 is clearly an A item, and items B390, H921, A211, and C003 are all C items. Other classifications are somewhat subjective, but one choice is to label E707 and F660 as A items, and D100 and G473 as B items. Annual Unit Cumulative Cumulative Item Demand Cost Volume volume percent E707 85 $2,000 $170,000 $170,000 48.04% F660 250 $320 $80,000 $250,000 70.64% D100 400 $100 $40,000 $290,000 81.94% G473 500 $75 $37,500 $327,500 92.54% B390 100 $90 $9,000 $336,500 95.08% H921 100 $75 $7,500 $344,000 97.20% A211 800 $9 $7,200 $351,200 99.24% C003 450 $6 $2,700 $353,900 100.00% $353,900 B) A local artisan uses supplies purchased from an overseas supplier. The owner believes the assumptions of the EOQ model are met reasonably well. Minimization of inventory costs is her objective. Relevant data, from the files of the craft firm, are annual demand (D) =150 units, ordering cost (S) = $42 per order, and holding cost (H) = $4 per unit per year (a) How many should she order at one time? (2 marks) (b) How many times per year will she replenish her inventory of this material?(1 mark) (c) What will be the total annual inventory (holding and setup) costs associated with this material (rounded to the nearest dollar)? (2 marks) (d) If she discovered that the carrying cost had been overstated, and was in reality only $1 per unit per year, what is the corrected value of EOQ?( 2 marks) Answer: (a) Q* = (b) (c) N= = 2.67 She should place about 2.67 orders per year. Setup costs = 2.67($42) = $112. Holding costs = (56.12/2)($4) = $112. Total costs = $112 + $112 = $224. At the lower value for H, the EOQ will be doubled to 112.25. (d) = 56.12. She should order 56 units at a time. QUESTION 5 A) A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution. (a) What is the probability that the system is empty? (1 mark) (b) What is the probability that there is precisely one vehicle in the system?(1 mark) (c) What is the probability that there are more than two vehicles in the system?(2 marks) (d) What is the probability of 5 or more vehicles in the system?(2 marks) Answer: (a) P0 = 1 - 5/8 = 0.375 (b) Pn> 1 = (5/8)2 = 0.391; the probability of exactly one is 1 - .391 - .375 = .234 (c) Pn> 2 = (5/8)2+1 = 0.244 (d) the probability of five or more is Pn > 4 = (5/8)5 = 0.0954. B) What combination of a and b will yield the optimum for this problem?(2 marks) Maximize $6a + $15b, subject to (1) 4a + 2b ≤ 16 and (2) 5a + 2b ≤ 20 and (3) a, b ≥ 0. Answer a = 0, b = 8 C) Suppose that the feasible region of a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be $X + $3Y what is the maximum profit the company can earn?(1 marks) Answer is $21