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Question 5 The following are four unadjusted seasonal indexes from time series data 1.029 .984 1.017 .993 By what number should each of the mean seasonal indexes be multiplied to arrive at seasonally adjusted indexes? Question 6 The seasonally adjusted quarterly indexes are as follows: 1.03 0.97 1.06 0.94 The unadjusted data for each of the four quarters are as follows: 825 725 865 802 What are the four seasonally adjusted values? Question 7 The value for the first quarter of the year is 68.47 The seasonal index is 89.75 What is the seasonally adjusted value for the first quarter? Question 9 The administrator of a small extended-can facility has compiled the following information regarding average prices for food purchases for the facility's kitchen (2007 - 100) Item 2007 2009 Dairy products 2.60 2.50 Meat 4.40 5.60 Vegetables 2.10 1.80 Fruit 2.00 2.30 What is the value of simple aggregate index? Question 10 What is the number of four-period centered moving averages of a time series with 20 time periods? Question 11 The owner of Maggie's Market received complaints that prices for fruit are constantly changing during the summer Using the following data, calculate the appropriate weighted aggregate price index for August, using June as the base period. Price per kg. Quantity sold (kg) Fruit June August June Apples $1.25 $1.50 80 Cantaloupes $1.00 $0.90 100 Cherries $0.80 $0.80 250 Peaches $1.50 $1.30 200 Watermekons $0.75 $0.50 300 Question 12 You are conducting a multiple regression using 5 independent variables and 50 sets of observations What are the degrees of freedom for the ANOVA table? Question 1 1. Which of the following statements is true? The inequality 3x1 + 2x2 ≤ 15 is represented on a graph by an area to the right of the straight line. Divisibility means that decision variables need not be integers. Additivity means that the constraints can be added. Proportionality means that the constraints are always used in the same proportion. Question 2 1. Which of the following statements is false? The expected monetary value makes use of the probabilities for each state of nature. The same optimal action is chosen regardless of whether the decision maker uses the expected monetary value or the expected opportunity loss approach. Bayes’ Law allows you to revise former probabilities based on new information. In a decision tree, a square node depicts the occurrence of a state of nature. Question 3 1. For the following linear programming problem, what are the values of x2 in the three extreme points? 400, 160, 0 720, 160, 0 720, 240, 0 720, 400, 0 Question 4 1. What is the intersection point for the two equations 3(x1) + 2(x2) = 16 and 4(x1) = 25 – 3(x2)? -11, -2 11, -2 -2, 11 2, 11 Question 5 1. Which of the following statements regarding linear programming is true? When maximizing the objective function, the optimal solution occurs at the extreme point closest to the origin. In order for an optimal solution to be feasible, at least one constraint must be non-binding. The number of constraints is dependent on the number of decision variables. If one objective coefficient moves outside of its range of optimality, the optimum value of more than one decision variable may change. Question 6 1. What is the intersection point for the two equations x1 + x2 = 8 and 2x1 – 2x2 = – 4? x1 = –3, x2 = –5 x1 = –3, x2 = 5 x1 = 3, x2 = -5 x1 = 3, x2 = 5 Question 7 1. What are the values of x1 and x2, respectively, for the intersection point of the following two equations? 2(x1) + 3(x2) = 15 3(x1) + 2(x2) = 20 -1, 6 1, 6 6, 1 15, -5 Question 8 1. What is implied in the statement that a resource is binding? It lacks a non-negativity restriction. There is more than one optimal solution. There is no incentive to acquire more of it. Its shadow price is greater than zero. Question 9 1. What is the maximum value of the objective function that has the following constraints? Objective function: $40x1 + $25x2 Subject to: x1 + x2 ≤ 40 3x1 + x2 ≤ 60 $800 $1,000 $1,150 $1,350 Question 10 1. What is the maximum value of the objective function that has the following constraints? $1,125 $1,200 $1,440 $1,800 Question 11 1. Which of the following statements about linear programming is false? Generally, you cannot use the two-dimensional graphical method to solve linear programming problems with more than two decision variables. One of the necessary assumptions in linear programming is additivity. This means that constraints can be added. The divisibility assumption means that the decision variables can assume non-integer values. The shadow price associated with a nonbinding constraint is always zero. Question 12 1. What is the intersection point for the two equations 2x1 + 4x2 = -4 and x1 - x2 = 4? x1 = -2, x2 = 2 x1 = 1, x2 = 4 x1 = 2, x2 = 4 x1 = 2, x2 = -2

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1) Labeled Question 5.
The seasonal indices need to be normalized.
(1/4) (1.029 + 0.984 + 1.017 + 0.993) = 1.00575
Each number needs to be multiplied by (1/1.00575) = 0.99428

2) Labeled Question 6.
825 / 1.03 = 800.971
725 / 0.97 = 747.423
865 / 1.06 = 816.038
802 / 0.94 = 853.191

3) Labeled Question 7.
68.47 / 0.897...
$40.00 for this solution

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