Problem 3-7 Freight car loadings over an 18-week period at a busy port are as fo

Question

Problem 3-7 Freight car loadings over an 18-week period at a busy port are as follows: Number 390 410 430 410 430 440 Number 480 520 560 540 580 620 Week 13 14 15 16 17 18 Number 630 640 680 700 720 740 Week Week 2 4 10 12 a. Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 2 decimal places.) Y343.6321.84t b. Use the above trend equation to predict expected loadings for Weeks 20 & 21 Round your final answers to 2 decimal places.) ted demand for Week 20 is 80227 and for Week 21 is 802.27 and for Week 21 is 780.43 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 28 Xx

Explanation / Answer

A

On the basis of above trend chart,

Y = 343.66 + 21.84*X

Or

Y = 343.63 + 21.84*X (As mentioned in the question)

B.

Forecasted demand for week 20 = 343.66 + 21.84*20 = 780.46

Forecasted demand for week 21 = 343.66 + 21.84*21 = 802.30

C.

When the weekly demand is 970 in week X,

970 = 343.66 + 21.84*X

X = (970-343.66)/21.84

X = 28.68 or 29th week

So, in week 29, the weekly demand will be 970.

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