14. Consider the matrix 1 4 2 A= 2 8 4 1 -4-2 a) Find a basis for ColA. b) Describe ColA geometrically. c) Find a basis for NulA. d) Describe NulA geometrically.
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- b. The following table shows the number of televisions sold over the last ten years at alocal electronic store.YEAR TV SALES1 1502 3003 4804 6005 6306 6407 7008 8259 90010 980i. Using trend projection, develop a formula to predict sales for years 11 and 12. Youhave to show all working. You will need to develop a table to calculate the slope andthe intercept. ii. Use that formula to forecast television sales for years 11 and 12.b. The following table shows the number of televisions sold over the last ten years at a local electronic store. YEAR 1 2 3 4 5 6 TV SALES 150 300 480 600 630 640 700 825 900 980 7 8 9 10 i. Using trend projection, develop a formula to predict sales for years 11 and 12. You have to show all working. You will need to develop a table to calculate the slope and the intercept. ii. Use that formula to forecast television sales for years 11 and 12.2. Calculate the forecasted sales revenue for May using the following data. Month Sales RevenueJanuary $ 11,000February $ 12,000March $ 14,000April $ 15,000 A. Use a 4-month weighted average to calculate forecasted May sales where the weights of the various months are as follows: January – 10%February – 20%March- 30%April- 40%
- To find the profit on the varying prices of a candy bar you will use: a. One variable Data Table b. Two variable Data Table c. Goal Seek d. None of theseB. The following table shows the number of televisions sold over the last ten years at a local electronic store. year TV sales 1 150 2 300 3 480 4 600 5 630 6 640 7 700 8 825 9 900 10 980 i. Using the trend projection, develop a formula to predict sales for years 11 and 12. Develop a table to calculate the slope and intercept. Please Show All Working. Use that formula to forecast television sales for years 11 and 12The table below shows the sales figures for a brand of shoe over the last 12 months.Months SalesJanuary 69February 75March 86April 92May 95June 100July 108August 115September 125October 131November 140December 150a. Using the following, forecast the sales for the months up to January the following year:-i. A simple three month moving average. ii. A three period weighted moving average using weights of 1, 2 and 3. Assign the highest weight to the most recent data. iii. Exponential Smoothing when α= .6 and the forecast for March is 350.iv. Determine which of the three forecasting technique is the most accurate using MAD.
- 25. Consider the following time series data: Quarter 1 234 Year 1 4 4235 2 5 Year 2 6357 5 7 Year 3 7 6 6 8 a. Construct a time series plot. What type of pattern exists in the data? b. Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. c. Compute the quarterly forecasts for next year.Consider the following time series data. Week 1 3 4 6. Value 18 13 16 11 17 14 a. Construct a time series plot. What type of pattern exists in the data? ( b. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7. ( c. Use a = .2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 7. . d. Compare the three-week moving average approach with the exponential smoothing approach using a = .2. Which appears to provide more accurate forecasts based on MSE? Explain. e. Use a smoothing constant of a = .4 to compute the exponential smoothing forecasts. Does a smoothing constant of .2 or .4 appear to provide more accurate forecasts based on MSE? Explain.The table below shows the sales figures for a brand of shoe over the last 12 months.Months SalesJanuary 69February 75March 86April 92May 95June 100July 108August 115September 125October 131November 140December 150 Using the following, forecast the sales for the months up to January the following year:- 1. Use exponential Smoothing when α= .6 and the forecast for March is 350.2. Determine which of the three forecasting technique is the most accurate using Mean Absolute Deviation MAD
- Consider the following time series data. Week 1 2 3 4 5 6 Value 19 14 16 12 17 15 A. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7 (to 2 decimals if necessary). MSE ______ The forecast for week 7 _______ B. Use a = 0.2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week (to 2 decimals). MSE _____ The forecast for week 7 ____ C. Use a smoothing constant of a = 0.4 to compute the exponential smoothing forecasts. Compute MSE (to 2 decimals).5) Consider the following tableau. Basic | Coefficients Vars x2 X3 X4 Const 1 -1 -3 -2 -1 1 -2 4 1 3 1 3 A) Label the basic variables (blank entries in the first column). B) Identify the entering (nonbasic) variable. C) Identify the exiting (basic) variable corresponding to your choice in part B. D) Perform a pivot based on your choices in B and C.Problem 7-19 eBook Given the linear program Max 3A +48 s.t. Y -1A+ 1A + 2A + s.t. 28 ≤ 8 2B ≤ 12 18 ≤ 16 Α, Β 2 0 a. Write the problem in standard form. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Al+ A+ A+C A+ B+ B B+ B B b. Select the correct graph that shows the optimal solution for the problem. S1 S1 + + S₂ + S2 + S3 53 A, B, S1, S2, S3 A Q☆
