ITM 501: Decision Analysis Homework Assignment 2 Instructions: - The assignment must be submitted through Blackboard. - Submit one spreadsheet file named according to the following format: _#2.xls (e.g. amir_gandomi #2.xls) - Create one worksheet for each question which clearly shows your analysis. Use the question number as the title of the worksheet. - Submissions that do not conform to these guidelines are subject to penalty. - Late submission penalty: 0.0694% per minute! Problem 1: Ryerson's admissions office is planning the admission policies for the entering freshman class of 2015. The university has a maximum of 4,500 available seats for freshman. Tuition fee is $8,600 for domestic students and $19,200 for international students. Ryerson wants to maximize its revenue from tuition, but by an Ontario mandate the total number of international students should be no more than 47% of the total number of students admitted. Also, each individual faculty in the university must have at least 30% domestic students in its freshman class. In order to improve its ranking, Ryerson is also planning to have a minimum average SAT score of 1150 among the admitted students. The following table shows the average SAT scores for last year's freshman class for domestic and international students (it is fair to assume that these averages remain the same for the new entering students). The table also shows the maximum size of the freshman class for each faculty. Faculty Faculty of Science Faculty of Arts Ted Rogers School of Management Faculty of Communication & Design Faculty of Engineering & Architectural Science Faculty of Community Services Average SAT Score Domestic International 1350 1460 1010 1050 1020 1110 1090 1180 1360 1420 1000 1400 Total Capacity 470 1300 240 820 1060 610 Questions: 1. Formulate an LP to determine the number of domestic and international students that should be admitted to each faculty. Clearly define your decision variables and formulate the objective function and constraints. Excel file, create a worksheet for this question (name it Q1) and write your answer in a text box. 2. How many domestic and international students should be admitted to each faculty and what is the maximum revenue? To answer this question, set up the model in Excel and find the optimal solution using Excel Solver. Continue to the next page ... ITM501 Amir Gandomi, Ph.D. Page 1 of 2 Problem 2: Samsonite is an American luggage manufacturer. One of their facilities makes three kinds of luggages: (1) Basic, (2) Premium, and (3) Luxury styles. Each luggage goes through four production stages: (1) cutting and coloring, (2) assembly, (3) finishing, and (4) quality control and packaging. The total number of hours available in each of these departments is 630, 600, 708, and 135, respectively. The sales revenue for each type of luggage is as follows: Basic $36.05, Premium $39.50, and Luxury $43.30. The material costs are Basic $6.25, Premium $7.50, and Luxury $8.50. The hourly cost of labor for each department is cutting and coloring $10, assembly $6, finishing $9, and quality and packaging $8. Each Basic luggage requires 0.7 hours of cutting and coloring, 0.5 hours of assembly, 1 hour of finishing, and 0.1 hours of quality and packaging. The corresponding numbers for each Premium luggage are 1 hour, 5/6 hours, 2/3 hours, and 0.25 hours, respectively. Likewise, the corresponding numbers for each Luxury luggage are 1 hour, 2/3 hours, 0.9 hours, and 0.4 hours, respectively. Questions: 3. Formulate an LP to determine the production plan that maximizes this facility's profits. Clearly define your decision variables and formulate the objective function and constraints. In your Excel file, create a worksheet for this question (name it Q3) and write your answer in a text box. 4. Set up the model in Excel and find the optimal solution using Excel Solver. 5. Answer the following questions (each question is independent of the others, all in one worksheet named Q5): a. What is the optimal production plan? Which of the resources are scarce? b. Suppose Samsonite is considering including a waterproofing process, the cost of which would be added directly to the price. Each Basic luggage would require 10 minutes of time in this process, each Premium luggage would need 15 minutes, and each Luxury luggage would need 20 minutes. Would the current production plan change as a result of this additional process if 170 hours of waterproofing time were available? Explain your answer. c. Suppose Samsonite is considering the possible introduction of a new product to its line of luggage: the Compact model. Market research suggests that Samsonite can sell the Compact model for $30. The amount of labor and the cost of raw materials for this new product are as follows: Cost Category Compact Cutting and coloring (hr.) Assembly (hr.) Finishing (hr.) Quality and packaging (hr.) Raw materials 0.5 0.75 0.75 0.2 $5.00 Use the pricing out strategy to check if this new model would be economically attractive to make. ITM501 Amir Gandomi, Ph.D. Page 2 of 2