Answer :
The exponential smoothing forecast for the next period is [tex]\( \boxed{\text{c. 100.6}} \).[/tex]
To calculate the exponential smoothing forecast for the next period, we use the formula:
[tex]\[ F_t = \alpha \times D_t + (1 - \alpha) \times F_{t-1} \][/tex]
Where:
- [tex]\( F_t \)[/tex] = forecast for the next period
- [tex]\( D_t \)[/tex] = actual demand for the current period
- [tex]\( F_{t-1} \)[/tex] = forecast for the previous period
- [tex]\( \alpha \)[/tex] = smoothing factor (given as 0.4)
Given:
- Actual demand [tex](\( D_t \))[/tex] = 103
- Previous forecast [tex](\( F_{t-1} \))[/tex] = 99
- Smoothing factor [tex](\( \alpha \))[/tex] = 0.4
Let's calculate:
[tex]\[ F_t = 0.4 \times 103 + (1 - 0.4) \times 99 \]\[ F_t = 0.4 \times 103 + 0.6 \times 99 \]\[ F_t = 41.2 + 59.4 \]\[ F_t = 100.6 \][/tex]
