the following table shows the sales data of a particular model of a dvd player. if the forecast sales for…
the following table shows the sales data of a particular model of a dvd player. if the forecast sales for may is 36.25, calculate the sales forecast for july using the simple exponential smoothing (ses) model with a smoothing constant of 0.40.\n|month|sales|\n|----|----|\n|jan|35|\n|feb|29|\n|mar|39|\n|apr|42|\n|may|51|\n|jun|56|\n\nthe sales forecast for july is more than 30 but less than or equal to 35.\nthe sales forecast for july is more than 35 but less than or equal to 40.\nthe sales forecast for july is more than 40 but less than or equal to 50.\nthe sales forecast for july is more than 50 but less than or equal to 55.
Answer
Explanation:
Step1: Recall SES formula
The simple - exponential - smoothing formula is $F_{t + 1}=\alpha A_t+(1 - \alpha)F_t$, where $F_{t + 1}$ is the forecast for the next period, $\alpha$ is the smoothing constant, $A_t$ is the actual value in period $t$, and $F_t$ is the forecast for period $t$.
Step2: Calculate forecast for June
We know that $\alpha = 0.40$, $A_{May}=51$, and $F_{May}=36.25$. $F_{June}=\alpha A_{May}+(1 - \alpha)F_{May}=0.4\times51+(1 - 0.4)\times36.25$. $F_{June}=0.4\times51 + 0.6\times36.25=20.4+21.75 = 42.15$.
Step3: Calculate forecast for July
We know that $\alpha = 0.40$, $A_{June}=56$, and $F_{June}=42.15$. $F_{July}=\alpha A_{June}+(1 - \alpha)F_{June}=0.4\times56+(1 - 0.4)\times42.15$. $F_{July}=22.4+25.29=47.69$.
Answer:
The sales forecast for July is more than 40 but less than or equal to 50.