Problem 2. Freight car loadings over a 12-year period at a busy port are as foll

Question

Problem 2. Freight car loadings over a 12-year period at a busy port are as follows: 15 16 17 500 510 310 12 541 a. b. c. Determine a linear trend line for expected freight car loadings. Use the trend equation to predict expected loadings for weeks 20 and 21 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 what week? Problem 3 After plotting demand for four periods, an emergency room manager has concluded that a trend- adjusted exponential smoothing model is appropriate to predict future demand. The initial estimate of trend is based on the net change of 30 for the three periods from 1 to 4, for an average of +10 units. Use = .5 and =.4, and TAF of 250 for period 5. Obtain forecasts for periods 6 through 10. 210 240 10

Explanation / Answer

PLEASE FIND BELOW ANSWER TO PROBLEM 2 :

Let the linear regression equation describing linear trend line is as follows :

Y = a + b.t

Y ( dependent variable ) = Number

T ( independent variable ) = Week number

A, b = constants

We place the values of week and number ( as provided ) in 2 adjacent columns in excel and apply the formula LINEST ( ) to obtain the values of a and b. Accordingly values of a and b are as follows :

A= 208.443

B = 18.995

Therefore,

Y = 208.443 + 18.995.t

a)Linear Trend line : 208.443 + 18.995.t

Answer to question b :

Expected loading for week 20 = 208.443 + 18.995 x 20 = 208.443 +379.9 = 588.343

Expected loading for week 21 = 208.443 + 18.995 x 21 = 208.443 + 398.895 = 607.338

Answer to question c :

Let the loading volume reach 800 loading per week during week t1

Accordingly ,

208.443 + 18.995.t1 = 800

Or, 18.995.t = 800 – 208.443

Or, 18.995.t = 591.557

Or, t = 31.14 ( 32 rounded to next higher whole number )

Loading volume will reach that level approximately during week 32

a)Linear Trend line : 208.443 + 18.995.t

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.