Freight car loadings over an 18-week period at a busy port are as follows: 35 We
ID: 425075 • Letter: F
Question
Freight car loadings over an 18-week period at a busy port are as follows: 35 Week Week Number 300 305 310 305 Number 365 395 425 420 450 480 Week 13 14 15 16 17 18 Number 485 490 540 545 550 10 14 points 310 315 12 00:52:10 a. Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 2 decimal places.) b. Use the above trend equation to predict expected loadings for Weeks 20 & 21. (Round your final answers to 2 decimal places.) References The forecasted demand for Week 20 is and for Week 21 is c. The manager intends to install new equipment when the volume exceeds 880 loadings per week. Assuming the current trend continues, in which week (at the earliest) should the loading volume reach that level? (Use the rounded answers, as required, from any previous part of this problem. Do not round any other intermediate calculations. Round your final answer to 2 decimal places.) It should reach 880 loadings in WeekExplanation / Answer
Where,
Y = Expected freight car loading
t = Week number 1.2.3, 4, 5 etc
a, b = Constants
We place values of “Week” and “Number” as provided in 2 different columns in excel and apply the formula LINEST ( ) to obtain values of a and b .
Accordingly corresponding values are :
A = 250.588
B = 17.745
Y = 250.588 + 17.745.t
Forecasted demand for week 20 ( by putting t = 20)
= 250.588 + 17.745 x 20
= 250.588 + 354.90
= 605.488 ( 605.49 rounded to 2 decimal places )
FORECASTED DEMAND FOR WEEK 20 = 605.49
Forecasted demand for week 21 ( by putting t = 21 )
= 250.588 + 17.745 x 21
= 250.588 + 372.645
= 623.233 ( 623.23 rounded to nearest whole number )
FORECASTED DEMAND FOR WEEK 21 = 623.23
Let 800 loading reach in week t1
Therefore ,
880 = 250.588 + 17.745.t1
Or, 17.745.t1 = 629.412
Or, t1 = 629.412/17.745 = 35.469 ( 35.47 rounded to 2 decimal places )
IT SHOULD REACH 880 LOADINGS IN WEEK 35.47
Y = 250.588 + 17.745.t
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