The Water Department of the city of Fort Worth, Texas, has topurchase untreated lake water from several administrative entitiesaround the city in order to fulfill the water requirements of itspopulation Most of the water is treated and pumped at one oftwo plants The Holly Water Treatment Complex and the RollingHills Plant The rolling Hills Plant is located on thesoutheast side of Fort Worth and is on a higher plain than thewest side Holly Treatment Plant Both plants are required tooperate in order to meet the citys demand however, the electricalcost of pumping water out of the Holly Treatment Plant isapproximately 15 higher than for the Rolling Hills Plant becauseof its lower elevation Because of the cost differential, thewater pumped from the tow plants has been slowly approaching a60 40 split in favor of the Rolling Hills Plant For budgetary reasons, the City Manager would like you toforecast the water processed and pumped at the Holly TreatmentPlant He will use your forecasts as a basis for estimatingthe associated electrical cost You are informed that waterconsumption varies from fall to spring and summer to winter There is also a gradual increase in the water demand at the HollyTreatment Plant because the total demand made by the population hasslowly increased Water Usage Data (in Tens of Millions of Gallons) Month 2001 2002 2002 2003 2003 2004 2004 2005 2005 2006 OCT 365 5 361 3 429 7 354 6 312 9 NOV 319 9 307 7 331 2 292 2 368 3 DEC 309 6 312 8 291 3 279 2 316 3 JAN 327 0 294 0 296 4 268 5 316 3 FEB 285 6 258 2 267 4 251 8 275 2 MAR 358 9 300 2 319 4 287 8 283 3 APR 326 5 402 3 350 2 336 4 286 2 MAY 324 6 367 3 447 4 350 6 352 7 JUNE 352 5 349 5 476 0 371 5 512 6 JULY 616 4 469 5 540 3 479 2 529 2 AUG 531 2 628 7 617 5 462 5 488 6 SEPT 403 6 428 7 429 9 421 0 461 4 Case Study Questions 1 Using the Data in the table, compute the centered movingaverages What is the benefit derived from obtaining thesemoving averages 2 Compute the seasonal indexes for each month When does theWater Department experience the larges seasonal effect Doesthis seem reasonable Does there seem to be a seasonalpattern 3 Deseasonalize the data and use the deseasonalized time series todetermine the linear trend equation What is the averageincrease in water use per month How far into the future doyou think the trend could be projected 4 Assuming a multiplicative model, obtain the cyclicalcomponents Does there seem to be a cyclical pattern 5 Prepare a forecast of water use in Fort Worth for the last threemonths of 2006 and the first month of 2007 using only the trendequation Use the seasonal indexes to adjust thedeseasonalized forecasts 6 In January 2007, the actual water use turned out to be 325 6 Discuss the forecasting error encountered here

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Mar 10, 2024

The Water Department of the city of Fort Worth, Texas, has topurchase untreated lake water from several administrative entitiesaround the city in order to fulfill

The Water Department of the city of Fort Worth, Texas, has topurchase untreated lake water from several administrative entitiesaround the city in order to fulfill the water requirements of itspopulation. Most of the water is treated and pumped at one oftwo plants – The Holly Water Treatment Complex and the RollingHills Plant. The rolling Hills Plant is located on thesoutheast side of Fort Worth and is on a higher plain than thewest-side Holly Treatment Plant. Both plants are required tooperate in order to meet the city’s demand; however, the electricalcost of pumping water out of the Holly Treatment Plant isapproximately 15% higher than for the Rolling Hills Plant becauseof its lower elevation. Because of the cost differential, thewater pumped from the tow plants has been slowly approaching a60-40 split in favor of the Rolling Hills Plant.

For budgetary reasons, the City Manager would like you toforecast the water processed and pumped at the Holly TreatmentPlant. He will use your forecasts as a basis for estimatingthe associated electrical cost. You are informed that waterconsumption varies from fall to spring and summer to winter. There is also a gradual increase in the water demand at the HollyTreatment Plant because the total demand made by the population hasslowly increased.

Water Usage Data
(in Tens of Millions of Gallons)

Month	2001-2002	2002-2003	2003-2004	2004-2005	2005-2006
OCT	365.5	361.3	429.7	354.6	312.9
NOV	319.9	307.7	331.2	292.2	368.3
DEC	309.6	312.8	291.3	279.2	316.3
JAN	327.0	294.0	296.4	268.5	316.3
FEB	285.6	258.2	267.4	251.8	275.2
MAR	358.9	300.2	319.4	287.8	283.3
APR	326.5	402.3	350.2	336.4	286.2
MAY	324.6	367.3	447.4	350.6	352.7
JUNE	352.5	349.5	476.0	371.5	512.6
JULY	616.4	469.5	540.3	479.2	529.2
AUG	531.2	628.7	617.5	462.5	488.6
SEPT	403.6	428.7	429.9	421.0	461.4

Case Study Questions

1. Using the Data in the table, compute the centered movingaverages. What is the benefit derived from obtaining thesemoving averages?

2. Compute the seasonal indexes for each month. When does theWater Department experience the larges seasonal effect? Doesthis seem reasonable? Does there seem to be a seasonalpattern?

3. Deseasonalize the data and use the deseasonalized time series todetermine the linear trend equation. What is the averageincrease in water use per month? How far into the future doyou think the trend could be projected?

4. Assuming a multiplicative model, obtain the cyclicalcomponents. Does there seem to be a cyclical pattern?

5. Prepare a forecast of water use in Fort Worth for the last threemonths of 2006 and the first month of 2007 using only the trendequation. Use the seasonal indexes to adjust thedeseasonalized forecasts.

6. In January 2007, the actual water use turned out to be 325.6. Discuss the forecasting error encountered here.