Consider the LP problem in Figure QP2.5 and refer to the Solver sensitivity report in Figure QP2.6. Min z = x1 + xX2 s.t. X1 – X2 2 0 (C1) X152 X2 2 1 X1 2 0 X2 2 0 (C2) (C3) (C4) (C5) Figure QP2.5 A B 6 Variable Cells D F G H 7 Final Reduced| Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease |SB$11 Solution x1 SC$11 Solution x2 1E+30 1E+30 9. 10 2 11 12 Constraints 13 Final Shadow Constraint Allowable Allowable 14 Cell Name Value Price R.H. Side Increase Decrease SD$5 C1 LHS SD$6 C2 LHS SD$7 C3 LHS 15 1 1 1E+30 1 1 16 1 2 17 1 1 Figure QP2.6 In which cell to find the shadow price of constraint C1? O E9 O F15 O F9 E15 8.
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- Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semifragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P13_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semifragile cargo.The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?Management of a home appliance store would like to understand the growth pattern of the monthly sales of Blu-ray disc players over the past two years. Managers have recorded the relevant data in the file P13_33.xlsx. a. Create a scatterplot for these data. Comment on the observed behavior of monthly sales at this store over time. b. Estimate an appropriate regression equation to explain the variation of monthly sales over the given time period. Interpret the estimated regression coefficients. c. Analyze the estimated equations residuals. Do they suggest that the regression equation is adequate? If not, return to part b and revise your equation. Continue to revise the equation until the results are satisfactory.
- The file P14_01.xlsx contains data on 100 consumers who drink beer. Some of them prefer light beer, and others prefer regular beer. A major beer producer believes that the following variables might be useful in discriminating between these two groups: gender, marital status, annual income level, and age. a. Use logistic regression to classify the consumers on the basis of these explanatory variables. How successful is it? Which variables appear to be most important in the classification? b. Consider a new customer: Male, Married, Income 42,000, Age 47. Use the logistic regression equation to estimate the probability that this customer prefers Regular. How would you classify this person?s/d/e/1FAIPQLSH RE8 IsdzdyqiPbivrqoOvnDclGNgCw_xVmiQO8kINDA/formResponse In the design of a jet engine part, the designer has a choice of specifying 10 either an aluminum alloy casting or a steel casting. Either material will provide equal service, but the aluminum casting will weigh 1.2 kg as compared with 1.35 kg for the steel casting. The aluminum can be cast for P 80.00 per kg. and the steel one for P 35.00 per kg. The cost of machining per unit is P 150.00 for aluminum and P 170.00 for steel. Every kilogram of excess weight is associated with a penalty of P 1,300 due to increased fuel consumption. Which material should be specified and what is the economic advantage of the selection per unit? Clue: Total Cost of using aluminum casting and steel casting and also how much will be saved. 1 Add fileA sample consists of 500 houses sold in Karachi between January 2020 and December 2020. The multiple linear regression analysis is carried out to predict the house prices for investment in residential properties in Karachi, Pakistan. The output below is produced using SPSS. (300 words) Table: Coefficients Model Unstandardized Coefficients t VIF Constant 14.208 5.736 Age of house -0.299 -2.322 1.58 Square footage of the house 0.364 2.931 1.71 Income of families in the area 0.004 0.392 1.01 Transportation time to major markets -0.337 -2.619 1.90 R2 = 0.67; DW = 2.08 Dependent Variable: House price (Pakistani rupees in Million) You are required to write the multiple regression How would you interpret the above ‘Output’ of a regression analysis performed in SPSS? From the above results, what can you say about the nature of autocorrelation? Is there multicollinearity in regression? How do you know?
- 4. ABC Dog Food Company located in Ottawa sells large bags of dog food to warehouse clubs. ABC uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 50 kilograms and a standard deviation of 1.25 kilograms. (a) What is the probability that a filled bag will weigh less than 49.5 kilograms? (b) What is the probability that a randomly sampled filled bag will weigh between 48.5 and 51 kilograms? (c) What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled? (d) ABC is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that 2% of all filled bags weigh more than 52 kilograms?! O A The following data relate the sales figures of the bar in Mark Kaltenbach's small bed-and-breakfast inn in Portland, to the number of guests registered that week: F1 Z 2 F2 a) The simple linear regression equation that relates bar sales to number of guests (not to time) is (round your responses to one decimal place): Bar Sales =+x guests b) If the forecast is 30 guests next week, the bar sales are expected to be $ (round your response to one decimal place). W S X H command # 3 80 F3 E D $ C 4 888 F4 R F I сла 5 V FS T G 6 B MacBook Air F6 Y Week 1 2 3 4 H & 7 44 F7 U N * 8 Guests 16 12 18 14 J DII FS I M ( 9 Bar Sales $340 $265 $375 $320 K DD F9 O V - < H 0 L 4 F10 command P V ^. : ; I 4 F11 { [ option + = ? I (1) F12 Next } 1 deleExplain these term Mixture of extreme value distribution. Modelling complex relationship between the variable. Lifetime model. (Please explain in your own wording so I can easily understand)
- For the next 6 numbers: Refer to the Management Scientist output of a maximization LP problem. The constraints are defined as follows: Constraint 1: advertising budget ( ) Constraint 2: sales force availability ( ) Constraint 3: production level (=) Constraint 4: retail stores requirement ( ) Optimal Solution Objective Function Value - Variable. Constraint X1 X2 X1 X2 X3 X4 X3 X4 1 2 Variable 1 2 3 3 4 OBJECTIVE COEFFICIENT RANGES 4 Constraint RIGHT HAND SIDE RANGES Value Slack/Surplus Lover Limit 25.000 425.000 150.000 0.000 84.000 50.000 No Lover Linit No Lover Linit Lover Limit 48450.000 0.000 25.000 0.000 0.000 4950.000 1775.000 515.000 0.000 Reduced Costs Dual Prices Current Value 90.000 84.000 70.000 60.000 Current Value 0.000 0.000 0.000 45.000 5000.000 1800.000 600.000 150.000 3.000 0.000 60.000 -17.000 Upper Limit No Upper Linit 90.000 87.000 105.000 Upper Linit 5850.000 No Upper Limit 603.571 200.000Based on the following regression ANOVA table, how many predictors are studied? Source df SS MS F Regression 4 1793.2356 448.3089 7.4854 Residual 45 2695.0996 59.8911 Total 49 4488.3352 1 3 4 5The following data are from a completely randomized design. In the following calculations, use ? = 0.05. Treatment1 Treatment2 Treatment3 63 82 68 46 73 55 54 88 60 37 61 45 xj 50 76 57 sj2 123.33 138.00 92.67 (a) Use analysis of variance to test for a significant difference among the means of the three treatments. State the null and alternative hypotheses. H0: At least two of the population means are equal.Ha: At least two of the population means are different. H0: ?1 = ?2 = ?3Ha: ?1 ≠ ?2 ≠ ?3 H0: Not all the population means are equal.Ha: ?1 = ?2 = ?3 H0: ?1 = ?2 = ?3Ha: Not all the population means are equal. H0: ?1 ≠ ?2 ≠ ?3Ha: ?1 = ?2 = ?3 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject H0. There is sufficient evidence…