Freight car loadings over an 18-week period at a busy port are as follows Week W

Question

Freight car loadings over an 18-week period at a busy port are as follows Week Week Number 270 290 310 290 310 320 Number 360 370 380 360 370 380 Week 13 14 15 16 17 18 Number 390 400 440 460 4 80 500 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.) The forecasted demand for Week 20 isand for Week 21 is c. The manager intends to install new equipment when the volume exceeds 850 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 850 loadings in Week

Explanation / Answer

Y = a + b.t

Where,

Y ( dependent variable ) = Expected freight car loadings

T ( independent variable ) = week number

A, b = constants

We place all the values of weeks and corresponding freight car loading numbers in 2 adjacent columns in excel and apply the formula LINEST( ) to obtain values of a and b.

Accordingly we obtain following values :

A= 256.01

B = 12.11

Therefore,

Y = 256.01 + 12.01.t

        Accordingly forecasted demand for week 20

      = 256.01 + 12.01 x 20

       = 256.01 +240.2

         =496.21

       Forecasted demand for week 21

     = 256.01 + 12.01 x 21

     = 256.01 + 252.21

     = 508.22

The forecasted demand for week 20 = 496.21

The forecasted demand for week 21 = 508.22

  

      Therefore,

850 = 256.01 + 12.01.t1

Or, 12.01.t1 = 593.99

Or, t1 = 593.99/12.01

Or, t1 = 49.45 ( 50 rounded to nearest whole number )

It should reach 850 loadings in week 50

The forecasted demand for week 20 = 496.21

The forecasted demand for week 21 = 508.22

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