IS 601 Assignment 7 1. The production of car tires in any given year is related to the number of cars produced that year and in prior years. Suppose our econometric model resulted in the following data. Regression Coefficient t-stat X 1 =Cars produced this year 5.00 10.4 X 2 =Cars produced last year 0.25 0.6 X 3 =Cars produced 2 years ago 0.67 1.4 X 4 =Cars produced 3 years ago 2.12 2.7 X 5 =Cars produced 4 years ago 3.44 6.5 Constant -50,000 Multiple R 0.83 a. Write out the regression equation. b. Which independent variable has the most significant effect on the production of car tires? c. What proportion of the total variation in the production of car tires is accounted for by the set of independent variables? 2. A multiple regression analysis showed the following ANOVA table result. Based on the information in the ANOVA, a. How many independent variables were included in the multiple regression analysis? b. What is the multiple coefficient of determination expressed as a percent? c. What is the decision regarding the global null hypothesis, at 0.05 significance level? 3. In a study of several companies going public for the first time, a researcher is particularly interested in the relationship between the size of the offering and the price per share. A sample of 15 companies that recently went public revealed the following information. Company Size ($ millions) x Price per Share y 1 9.0 10.8 2 94.4 11.3

IS 601 3 27.3 11.2 4 179.2 11.1 5 71.9 11.1 6 97.9 11.2 7 93.5 11.0 8 70.0 10.7 9 160.7 11.3 10 96.5 10.6 11 83.0 10.5 12 23.5 10.3 13 58.7 10.7 14 93.8 11.0 15 34.4 10.8 Use a software to: a. Determine the regression equation. b. Conduct a test to determine whether size is a significant variable in describing the price per share. (use alpha 0.05) c. Determine the coefficient of determination. Do you think the researcher should be satisfied with using the size of the offering as the independent variable? Include a copy of your software analysis. 4. An insurance company is introducing two new product lines: special risk insurance and mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit on mortgages. The management wishes to establish sales quotas for the new product lines to maximize total expected profit. The work requirements are as follows: a. Formulate a linear programming model for this problem. b. Use the graphical method to solve this model. c. Use Excel solver to solve this problem (include a copy of the software analysis). 5. A company produces two light fixtures (products 1 and 2) that require both metal frame parts and electrical components. Management wants to determine how many units of each product to produce so as to maximize profit. For each unit of product 1, 1 unit of frame parts and 2 units of electrical components are required. For each unit of product 2, 3 units of frame parts and 2 units of electrical components are required. The company has 200 units of frame parts and 300 units of electrical components. Each unit of product 1 gives a profit of $1, and each unit of product 2, up to 60 units, gives a profit of $2. Any excess over 60 units of product 2 brings no profit, so such excess has been ruled March 12, 2002 MATH 428 Exam I Spring Semester, 2002 Name: Score: 1(30pts) The Primo Insurance Company is introducing two new product lines: special risk insurance and mortgages. The expected profit is $5 per unit on special risk insurance and $2 per unit on mortgages. The management wishes to establish sales quotas for the new product lines to maximize total expected profit. The work requirements are as follows: Work-Hours per Unit Department Special Risk Mortgage Work-Hours Available Underwriting 3 2 2400 Administration 0 1 800 Claims 2 0 1200 (a) Determine the decision variables and formulate a linear programming model for this problem. (b) Use the graphical method to find the optimal solution. (c) Determine the shadow price with respect to underwriting. (d) Identify unbinding constraint(s). (e) Let x 3 , x 4 , x 5 be the slack variables. What do x i = 0, i = 3, 4, 5 mean graphically? (It suffices to label these equations on your graph above.) (f) Formulate the 0 iteration of the tabular form of the simplex method and complete the first iteration of the tabular form. Identify the CPF solution. (g) Use the information from the graphical method above to determining the basic variables and the nonbasic variables at the (would be) final iteration of the tabular form of the simplex method. (h) (Bonus 5 pts) If 100 work-hours were shifted from the Department of Administration to the Department of Underwriting, what would be the increase in profit? 2(10pts) Consider the game having the following payoff table. Player 2 Strategy 1 2 3 4 1 0 -3 -2 -4 Player 1 2 -4 -2 -1 1 3 1 -1 2 0 (a) Use the minimax criterion to find the best strategy for each player. Is it a stable game?

IS 601 out. a. Formulate a linear programming model for this problem. b. Use Excel solver to solve this problem (include a copy of the software analysis). 6. A group of young students earns a (temporary) steady living by picking up discounted items from electronic stores ($10 per piece) and reselling them. Each item has a street value, a weight, and a volume; there are limits on the number of available items, and on the total weight (< 500 pounds) and volume (< 300 cubic feet) that can be managed at one time. Values, weights, volumes, and available numbers are given below. Formulate a LP problem and solve it with Excel Solver to find out how many of each item the students should pick and resell (include a copy of the software analysis).