Question

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

Week	Number	Week	Number	Week	Number
1	220	7	350	13	460
2	245	8	360	14	475
3	280	9	400	15	500
4	275	10	380	16	510
5	300	11	420	17	525
6	310	12	450	18	541

   
a. Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 3 decimal places.)

YˆY^ =  +  t

b. Use the trend equation to predict expected loadings for weeks 20 and 21. (Round your intermediate calculations and final answers to 3 decimal places.)

The forecasted demand for week 20 and 21 is  and  respectively.

c. The manager intends to install new equipment when the volume exceeds 800 loadings per week. Assuming the current trend continues, the loading volume will reach that level in approximately how many more weeks? (Round your intermediate calculations to 3 decimal places and final answer to the nearest whole number.) *I asked this question before and 31 was not correct for number of weeks*

It would take approximately  more weeks.

Answer 1

a) Determine a linear trend line for expected freight car loadings

Y=19X+208.5

where y= car loadings x= week number

b)Use the trend equation to predict expected loadings for weeks 20 and 21

Week 20: Y=19*20+208.5

= 588.5

Week 21 : Y= 19*21+208.5

=607.5

c. The manager intends to install new equipment when the volume exceeds 800 loadings per week.

Here is the working

since

Y=19X+208.5

so substituting Y=800 we get this

800=19X+208.5

800-208.5=19x

591.5=19X

Now X= 591.5/19

=31.131 weeks