ASSIGNMENT-1 QUANTITATIVE METHODS (STAT-201) Student Full Name: Student ID: CRN No.: Note: 1. All the questions are compulsory. 2. Due date: Oct. 21, 2016 until 11:59 P.M. 3. Points: Section-I 16=6 Section-II 16=6 Section-III 63=18 Total 30 Section-I State whether the following statements are True or False. (16 = 6) 1. Define the problem is the first step in quantitative analysis. a) True b) False 2. Sensitivity analysis helps us estimate the effect of known and unknown errors in our model. a) True b) False 3. Minimum EOL will always equal EVwPI. a) True b) False 4. When using the EOL as a decision criterion, the best decision is the alternative with the largest EOL value. a) True b) False 2 5. The most common quantitative causal model is regression analysis. a) True b) False 6. Time-series models enable the forecaster to include specific representations of various qualitative and quantitative factors. a) True b) False Section-II Circle/tick the right answer from the answers given below. (16 = 6) 1. Which of the following is not a quantitative factor: a) Inventory levels b) Technological breakthroughs c) Demand d) Labor cost. 2. Expressing profits through the relationship among unit price, fixed costs, and variable costs is an example of a) a sensitivity analysis model. b) a quantitative analysis model. c) a post-optimality relationship. d) a parameter specification model. 3. A pessimistic decision-making criterion is a) maximax. b) maximin. c) decision making under certainty. d) minimax regret. 4. In assessing utility values, a) the worst outcome is given a utility of -1. b) the best outcome is given a utility of 0. c) the worst outcome is given a utility of 0. d) the best outcome is given a value of -1. 5. Which of the following is a technique used to determine forecasting accuracy? a) moving average b) exponential smoothing c) mean absolute percent error d) Delphi method 6. Which of the following is not considered to be one of the components of a time series? a) Trend b) Seasonality c) Cycles 3 d) variance Section-III Answer the following Essay Type Questions (63=18) 1. Mug Co is a new company, which manufactures personalized imprinted mugs. Rental costs of its equipment and its local totaled $1800. The materials used in one mug cost $9, and the selling price is $15 each. a) How many mugs must Mug Co sell to break-even? What is the total revenue for this? b) What would be the selling price per unit for a break-even of 200? 2. The following payoff table provides profits based on various possible decision alternatives and various levels of demand. States of Nature Demand Alternatives Low Medium High Alternative 1 70 110 130 Alternative 2 80 80 80 Alternative 3 25 60 140 The probability of a low demand is 0.4, while the probability of a medium and high demand is each 0.3. a) b) c) d) What decision would an optimist make? What decision would a pessimist make? What is the highest possible expected monetary value? Calculate the expected value of perfect information for this situation. 3. The ABC Co. is considering a new consumer product. They have no idea whether or not the XYZ Co. will come out with a competitive product. If ABC adds an assembly line for the product and XYZ does not follow with a competitive product, their expected profit is $40,000; if they add an assembly line and XYZ does follow, they still expect a $10,000 profit. If ABC adds a new plant addition and XYZ does not produce a competitive product, they expect a profit of $600,000; if XYZ does compete for this market, ABC expects a loss of $100,000. Calculate Hurwicz's criterion of realism using 's of a. 0.7, b. 0.3, and c. 0.1. 4. Mark M. Upp has just been fired as the university book store manager for setting prices too low (only 20 percent above suggested retail). He is considering opening a competing bookstore near the campus, and he has begun an analysis of the situation. 4 There are two possible sites under consideration. One is relatively small, while the other is large. If he opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is low, he will lose $10,000. If he opens at Site 2 and demand is high he will generate a profit of $80,000, but he will lose $30,000 if demand is low. He also has decided that he will open at one of these sites. He believes that there is a 50 percent chance that demand will be high. He assigns the following utilities to the different profits: U ( 50000 )=? U (10000 )=0.22 U ( 80000 )=1 U (30000 ) =0 For what value of utility for $50,000, U(50000), will Mark be indifferent between the two alternatives? 5. For the data below: Month January February March April May June Automobile Battery Sales 20 21 15 14 13 16 Month July August September October November December Automobile Battery Sales 17 18 20 20 21 23 a) Develop a three-month moving average. b) Compute MAD. 6. Use simple exponential smoothing with = 0.33 to forecast the tire sales for February through May. Assume that the forecast for January was for 22 sets of tires. Month January February March April Automobile Battery Sales 28 21 39 34