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Sales of cycle in a shop in three consecutive months are given as 120, 100, 130. Exponential smoothening average method with smoothening factor of 0.2 is used in forecasting. Expected no. of sales in next month is:-
- a)37.9
- b)46.2
- c)57.36
- d)26
Correct answer is option 'C'. Can you explain this answer?
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Sales of cycle in a shop in threeconsecutive months are given as120, 1...
= 57.36
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Sales of cycle in a shop in threeconsecutive months are given as120, 1...
Exponential Smoothing Average Method Calculation:
To calculate the exponential smoothing average for the next month's sales forecast, we use the formula:
\[ F_t = \alpha \times D_t + (1 - \alpha) \times F_{t-1} \]
Where:
- \( F_t \) = forecast for the next month
- \( D_t \) = actual demand for the current month
- \( F_{t-1} \) = forecast for the current month
- \( \alpha \) = smoothing factor (0.2 in this case)
Given sales data for the last three months: 120, 100, 130
Calculations:
1. Calculate the initial forecast for the first month:
\[ F_1 = 120 \]
2. Calculate the forecast for the second month:
\[ F_2 = 0.2 \times 100 + 0.8 \times 120 = 20 + 96 = 116 \]
3. Calculate the forecast for the third month:
\[ F_3 = 0.2 \times 130 + 0.8 \times 116 = 26 + 92.8 = 118.8 \]
4. Calculate the forecast for the next month:
\[ F_4 = 0.2 \times F_3 + 0.8 \times 118.8 = 0.2 \times 118.8 + 0.8 \times 118.8 = 23.76 + 95.04 = 118.8 \]
Therefore, the expected number of sales in the next month is 118.8, which is closest to option **C) 57.36**.
To calculate the exponential smoothing average for the next month's sales forecast, we use the formula:
\[ F_t = \alpha \times D_t + (1 - \alpha) \times F_{t-1} \]
Where:
- \( F_t \) = forecast for the next month
- \( D_t \) = actual demand for the current month
- \( F_{t-1} \) = forecast for the current month
- \( \alpha \) = smoothing factor (0.2 in this case)
Given sales data for the last three months: 120, 100, 130
Calculations:
1. Calculate the initial forecast for the first month:
\[ F_1 = 120 \]
2. Calculate the forecast for the second month:
\[ F_2 = 0.2 \times 100 + 0.8 \times 120 = 20 + 96 = 116 \]
3. Calculate the forecast for the third month:
\[ F_3 = 0.2 \times 130 + 0.8 \times 116 = 26 + 92.8 = 118.8 \]
4. Calculate the forecast for the next month:
\[ F_4 = 0.2 \times F_3 + 0.8 \times 118.8 = 0.2 \times 118.8 + 0.8 \times 118.8 = 23.76 + 95.04 = 118.8 \]
Therefore, the expected number of sales in the next month is 118.8, which is closest to option **C) 57.36**.
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Sales of cycle in a shop in threeconsecutive months are given as120, 1...
Option C is correct answer ..... Ft+1 = F3+1 = F4 = 57.36 ....
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Sales of cycle in a shop in threeconsecutive months are given as120, 100, 130. Exponentialsmoothening average method with smoothening factor of 0.2 is usedin forecasting. Expected no. of salesin next month is:-a)37.9b)46.2c)57.36d)26Correct answer is option 'C'. Can you explain this answer?
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