Question

Maya sells magaritas and collected sales data for the past few days. Calculate the forecast for Day 3 by exponential smoothing, using a = 0.8. Remember that we start exponential smoothing with F₂ = A₁.

Day 1 2
Sales 99 107

Answer 1

The forecast for Day 3 using exponential smoothing with a smoothing constant (a) of 0.8 is 105.4.

Step-by-step explanation:

To calculate the forecast for Day 3 using exponential smoothing, we'll follow the formula Ft+1 = αAt + (1-α)Ft, where Ft+1 is the forecast for the next period, α is the smoothing constant (0.8 in this case), At is the actual sales value at time t, and Ft is the forecast value at time t. Given that F2 = A1, the initial forecast for Day 2 is equal to the actual sales on Day 1, which is 99. Now, we use the Day 2 actual sales and the smoothing constant to calculate the forecast for Day 3:

F3 = 0.8×107 + (1-0.8)×99
F3 = 85.6 + 19.8
F3 = 105.4

Therefore, the forecast for Day 3, using exponential smoothing with α = 0.8, is 105.4.