BSc (Hons) Business Information Systems. Examinations for / Semester 2

Transcription

1 BSc (Hons) Business Information Systems Cohort: BIS/14B/FT Examinations for / Semester 2 MODULE: QUANTITATIVE ANALYSIS FOR BUSINESS MODULE CODE: Duration: 3 Hours Instructions to Candidates: 1. Answer ALL questions. 2. Questions may be answered in any order but the question number should be clearly stated. 3. New question should be started on a fresh page. 4. All workings should be clearly shown. 5. The Normal Distribution table, the Z-Chart & Loss Function table and the Factor for Control Chart table are enclosed. 6. The total mark is 100. This question paper contains 9 questions and 11 pages. Quantitative Analysis for Business Page 1 of 11 [P.T.O]

2 QUESTION 1: (11 Marks) ANSWER ALL QUESTIONS Profits as a function of sales potential and crutch size are given as follows: Crutch size Sales Potential Probability Small Regular Large Excellent 0.3 $62,500 $100,000 $50,000 Good 0.4 $25,000 $55,000 $25,000 Poor 0.3 -$37,500 -$7,500 $2,500 (a) Determine the best policy based on the i) Pessimistic rule. ii) Optimistic rule. (b) Construct the decision tree for the situation. (c) Referring to your answer in part (b) above, determine the best policy. ( = 11 marks) QUESTION 2: (8 Marks) Mr. Tom, a biologist, assumes that there is a linear relationship between the amounts of fertilizer supplied to tomato plants and the subsequent yield of tomatoes obtained. Eight tomato plants of the same variety were selected at random and treated, weekly, with a solution in which x grams of fertilizer were dissolved in a fixed quantity of water. The yield y kilograms of tomatoes were recorded. Quantitative Analysis for Business Page 2 of 11 [P.T.O]

3 X Y (a) Calculate the equation of least square regression line of y on x. (b) Using your answer in part (a), estimate: i) The yield of a plant treated weekly with 3.7 grams of fertilizer. ii) The amount of fertilizer that will be needed to obtain a yield of 7.5Kg of tomatoes. QUESTION 3: (25 Marks) ( = 8 marks) (a) Give one advantage and one disadvantage of the moving average forecasting method. (b) Given a time series data, explain your selection criterion for choosing a multiplicative or an additive decomposition model. (c) For the data in Table 1 Table 1: Sales for Quarters Quarters i) Give the plot of the sales figures. ii) Justifying your selection, choose either the multiplicative or the additive decomposition model to obtain the equation to the model trend as: Y t = t. ( = 25 marks) Quantitative Analysis for Business Page 3 of 11 [P.T.O]

4 QUESTION 4: (10 Marks) Consider the following set of data for manufacturing employment (in thousands). Year Actual Year Actual Using the exponential smoothing with α = 0. 9, obtain the forecast for QUESTION 5: (8 Marks) (10 marks) Consider the M/M/1 queuing problem where Ally, the mechanic at International Muffler Shop, is able to install new mufflers at an average of 3 per hour. Customers seeking this service arrive at the shop on the average of 2 per hour. They are served on a First-In First-Out basis and come from a very large population of possible buyers. Based on the description given above, find: (a) (b) (c) (d) The average number of cars in the system. The average time a car spends in the system. The average number of cars waiting in the queue. The probability that there are more than 3 cars in the system. ( = 8 marks) Quantitative Analysis for Business Page 4 of 11 [P.T.O]

5 QUESTION 6: (13 Marks) (a) The daily demand for a commodity is approximately 100 units. Every time an order is placed, a fixed cost of $100 is incurred. The daily holding cost per unit inventory is $0.02. If the lead time is 13 days, determine: i) The Economic Order Quantity. ii) The minimal inventory cost. iii) The reorder point and interpret your answer. (b) Suppose the South-East Mechanic Company has a product for which the assumption of the EOQ inventory model with backorders are valid. Information obtained by the company are as follows: Annual demand = 2000 units/ year. The cost per order = $ 25. The holding Cost = $ 10 per unit per year. The backorder cost = $ 30 per unit per year. Determine: i) The optimal order quantity. ii) The optimal backorder level. iii) The cycle time. ( = 13 marks) Quantitative Analysis for Business Page 5 of 11 [P.T.O]

6 QUESTION 7: (7 Marks) Tommy Chemical Company has a contract with its customer to supply a unique chemical product. Historically, the customer places order approximately every 6 months. Since chemical needs 2 months ageing time, Tommy Chemical Company will have to make its production quantity decision before the customer places an order. Tommy s inventory problem is to determine the number of Kilograms of chemical to produce in anticipation of customer s order. Detailed information: Manufacturing cost: $15/Kg Selling price: $20/Kg Underestimation (Tommy Chemical Company to buy substitute + transportation cost): $24/Kg Overestimation (Tommy Chemical Company to reprocess and sell the surplus): $5/Kg An analysis of Tommy s chemical demand shows that demand follows a normal probability distribution and with mean μ = 1000 Kg and standard deviation σ = 100. Required: Compute the optimal production quantity of chemical to be produced by Tommy Chemical Company. (7 marks) QUESTION 8: (10 Marks) A quality control inspector at the Cocoa Fizz soft drinks has taken twenty-five samples with 4 observations each of the volume of the bottles filled. The data and the computed means are shown in the following table: Quantitative Analysis for Business Page 6 of 11 [P.T.O]

7 (a) If the standard deviation of the bottling is 0.14 ounces, use this information to develop the control limits of three standard deviations for the bottling operation. (b) Use of the sample range to estimate variability can also be applied to the bottling operation. A quality control inspector at Cocoa Fizz is using the data from the above table. If the average range for the twenty-five samples is 0.29 ounces, develop three-sigma control limits for the bottling operation. Sample Observation (Bottle volume in ounces ) Average Range Number R Total (c) The quality control inspector would like to develop a range chart in order to monitor volume dispersion in the bottling process. Use the data form the above table to develop control limits for the sample range. ( = 10 marks) Quantitative Analysis for Business Page 7 of 11 [P.T.O]

8 QUESTION 9: (8 Marks) (a) Three bottling machines at Cocoa Fizz are being evaluated for their capability: Bottling Machine Standard Deviation A 0.05 B 0.1 C 0.2 If specifications are set between 15.8 and 16.2 ounces, determine which machines are capable of producing within specifications. (b) Compute the Cpk measures of process capability for the following machines and interpret the findings. What value would you have obtained with the Cp measure? Machines Data: USL = 110 LSL = 50 Process σ = 10 Process µ = 60 (4 + 4 = 8 marks) ***END OF QUESTION PAPER*** Quantitative Analysis for Business Page 8 of 11 [P.T.O]

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