Question

Freight car loadings over an 18-week period at a busy port are as follows. Week 13 14 15 16 17 18 Week 1 Number 280 295 310 295 310 320 Week Number 350 400 450 435 485 535 Number 545 585 600 615 630 10 12 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 860 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 860 loadings in Week

Answer 1

We use excel to answer the question as shown below:

We prepare the table as given below:

2 Week Number 4 280 295 310 295 310 320 350 400 450 435 485 435 6 3 y 22.864x + 221.41 9 10 11 8 12 9 13 10 14 11 15 12 16 13 17 14 18 15 19 16 20 17 21 18 22 19 23 20 24 21 25 22 26 500 585 600 615 630 0 1 2 3 45 6 78 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Weeks

a) As seen from above, the equation of the line is y = 221.41 + 22.87 t

b) To find out forecast demand:

We calculate as shown in table below:

y-221.41+22.87X 280 295 310 295 310 320 350 400 450 435 485 435 545 2 4 7 10 12 13 1A 15 16 17 18 19 20 21 600 615 630 655.94 678.81 724.55

Hence, the forecast demand for Week 20 = 678.81 and for week 21 is 701.68

c. For reaching 860 loading, we extend the table till it reaches 860,

Week Number Equation y 221.41+22.87X 2汝) 295 310 295 310 320 350 3 4 9 450 435 485 435 545 10 12 13 14 15 16 17 18 19 585 615 630 678.81 701.68 724.55 747.42 770.29 793.16 816.03 838.9 861.77 884.64 21 23 24 25 26 27 28 29 30

As seen from above, it should reach 860 in week 29.