Question

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

Week	Number	Week	Number	Week	Number
1	370	7	415	13	450
2	380	8	425	14	455
3	390	9	435	15	475
4	380	10	425	16	485
5	390	11	435	17	495
6	395	12	445	18	505

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

YˆY^ =  +  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 950 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 950 loadings in Week              .

Answer 1

ANSWER:

Given that,

b = (1392210-1325250)/(37962-29241) = 7.68

a = (7750-7.68*171)/18 = 357.61

y = 357.61 + 7.68*t

b)

For week 20, y = 357.61 + 7.68*20 = 511.17

Week 21, y = 357.61 + 7.68*21 = 518.85

c)

950 = 357.61 + 7.68*t

t = 77.13

So, it will reach 950 on week 77.13