Freight car loadings over an 18-week period at a busy port are as follows: a. De

Question

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

a. Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 2 decimal places.)

Y=__+__t

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 is              and for Week 21 is              .

c. The manager intends to install new equipment when the volume exceeds 970 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 970 loadings in Week              .

Week Number Week Number Week Number 1 390 7 480 13 630 2 410 8 520 14 640 3 430 9 560 15 680 4 410 10 540 16 700 5 430 11 580 17 720 6 440 12 620 18 740

Explanation / Answer

Let ,

Y = A + B .t

Where,

T ( independent variable ) = week number

Y ( Dependent variable ) = Forecasted value of freight car loading

A, B = constants

We place values of Week number as well as corresponding number of freight car loading in two parallel columns in excel and apply the formula LINEST ( )

Accordingly , we obtain following values of a and b :

A = 343.66

B = 21.84

Therefore , Y = A + B.t = 343.66 + 21.84.t

Y = 343.66 + 21.84.t

Answer to question b :

Forecasted demand for week 20 = 343.66 + 21.84 x 20 = 343.66 + 436.8 = 780.46

Forecasted demand for week 21 = 343.66 + 21.84 x 21 = 343.66 + 458.64 -= 802.30

Answer to question c :

Let the week at which loading volume exceeds 970 freight cars = t1

Therefore ,

343.66 + 21.84.t1 > 970

Or, 21.84.t1 > 626.34

Or, t1 > 28.67

LOADING VOLUME SHOULD REACH LEVEL OF 970 AT WEEK 28.67

Y = 343.66 + 21.84.t

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