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operations research1 - linear programming - assignment
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- B. The owner of a small hardware store has noted a sales pattern that seems to parallel the number of break-inns reported each week in newspaper. The 08 02 05 Sales: 50 22 24 18 35 42 13 Break-inns: 9 04 04 06 08 03 7 Estimate sales when break-inns is 7» 95 A cosmetics manufacturer's marketing department has developed a linear trend equation that can be used to predict annual sales of its popular Hand & Foot Cream. Ft = 80 + 25t where Ft = Annual sales (000 bottles), t is in years. Predict annual sales for year 6? 170 230 10 % 6 52 min 42 secst sales 1 324 2 245 3256 4 567 5 346 6 357 7 357 8 257 9 1678 What is the predicted future sales for time period 13?
- A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage Industry and collects monthly data for 25 firms. He estimates the model Sales-o Advertising. The following ANOVA table shows a portion of the regression results. Regression Residual df 1 23 55 78.53 504.02 MS 78.53 21.91 T 3.581. Solve manually. a. Income at the law firm Smith and Wesson for the period February to July was as follows: Month Feb Mar Аpr May June July Income $ 70.00 71.30 (in thousand) 68.50 64.30 71.70 72.8 Use trend-adjusted exponential smoothing to forecast the law firm's August income. Assume that the initial forecast for February is $65,000 and the initial trend adjustment is 0. The smoothing constants selected are alpha = 0.1 and beta = 0.2 %3D1. A commercial bakery has recorded sales (in dozens) for three products, shown as follows:DayBlueberryMuffinsCinnamonBuns Cupcakes1 30 18 452 34 17 263 32 19 274 34 19 235 35 22 226 30 23 487 34 23 298 36 25 209 29 24 1410 31 26 1811 35 27 47 DayBlueberryMuffinsCinnamonBuns Cupcakes12 31 28 2613 37 29 2714 34 31 2415 33 33 22a. Predict orders for the following day for each of the products using an appropriate naive method.Hint: Plot each data set.
- 35. The Mr. Meadows Cookie Company can obtain accurate forecasts for 12 months based on firm orders. These forecasts and the number of workdays per month are as follows: Demand Forecast Month (in thousands of cookies) Workdays 1 850 26 2 1,260 24 3 510 20 4 980 18 770 22 850 23 7 14 1,050 1,550 1,350 1,000 970 680 21 9. 23 10 24 11 21 12 13 During a 46-day period when there were 120 workers, the firm produced 1,700,000 cookies. Assume that there are 100 workers employed at the beginning of month 1 and zero starting inventory. a. Find the minimum constant workforce needed to meet monthly demand. b. Assume cz= $0.10 per cookie per month, cH= $100, and cp = $200. Add columns that give the cumulative on-hand inventory and inventory cost. What is the total cost of the constant workforce plan? c. Solve for the optimal plan using linear programming. Compare your solution to b.7. Block Commodities has gathered the following information concerning rock salt deliveries to its clients, which it believes are highly seasonal: (Noteshaper Scenarios #31) Month Year 1 Year 2 Year 3 Year 4 Avg Monthly January 75 76 95 117 90.6 February 48 34 34 52 42.0 March 35 48 12 56 37.8 April 22 34 35 25 29.0 May 2 12 1 5.3 June 3 10 5.0 July 28 33 35 28 31.0 August 145 98 109 120 118.2 September 181 197 162 145 171.1 October 190 201 220 180 197.8 November 100 101 110 98 102.3 December 81 70 87 88 81.6 Total 910 904 913 920 a) What is the value of the seasonal relative for July and December? b) Block Commodities believes that next year it will deliver 1,200 tons of rock salt (up from the approximately 900 delivered in past years). Using the seasonal relatives, forecast the demand in tons of rock salt for May and October of next year.6. Tread-On-Us Carpet & Tile Company sold 700,000 square f.et of carpet last year, 800,000 square feet the year before, and 600,000 square a. Using a three-year moving average, predict carpet sales for this year. b. Then, assuming actual sales for this year turn out to be 780,000 square feet, predict sales for next year. feet the year before that.
- 10 171 a) Calculate the three-period moving-average forecast for periods 7 through 10. Three-period Period Actual moving average 1 64 84 91 4 97 115 6. 135 7 137 8. 144 6. 153 10 171 b) Calculate the weighted moving average for periods 7 through 10 using weights of 0.6, 0.3, ar 0.1. 02:40 A a ENGQ1: Income at the architectural firm Spraggins and Yunes for the period February to July was as follows: Month February March April May June July 72.8 Income (in $ 70.0 thousand) 68.5 64.5 71.7 71.3 Use trend-adjusted exponential smoothing to forecast the firm's August income. Assume that the initial forecast average for February is $65,000 and the initial trend adjustment is 0. The smoothing constants selected are a = .1 and B =.2.Quarter 1 2 31 11 14 172 20 23 263 29 32 354 38 41 44Compute seasonal relatives for this quarterly data.a. Use the SA method.