For a given data group, simple exponential smoothing is being used to forecast demand. The forecast of a given period is 110, which turned out to be 4 units more than actual demand. The forecast for next period is 109.2. Based on information given, what is smoothing constant, alpha? Select one:

a. 0.20
b. 0.10
c. 0.15
d. None of the choices
e. 0.60

The smoothing constant alpha is 0.20 (Option a)

Step-by-step explanation:

To solve this problem, first we write the succession of the simple exponential smoothing:

Where s(t) is the forecast for period t, s(t-1) is the forecast for period (t-1), xt is the real demand for period t, and alpha is the smoothing constant.

All but the alpha constant are known

s(t)=109.2

s(t-2)=110

xt=110-4=106

Then, we can calculate alpha as:

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.