Final Answer:
The simple exponential smoothing forecast for the 4th week with α=0.3 is 48.2.
Step-by-step explanation:
Simple exponential smoothing is a technique used to forecast data points by giving more weight to recent data. The formula for simple exponential smoothing is F_t+1 = α D_t + (1-α) F_t, where F_t+1 is the forecast for the next period, D_t is the actual demand for the current period, F_t is the forecast for the current period, and α is the smoothing constant.
Given that α=0.3 and the data for the first three weeks are 50, 45, and 55 respectively, we can calculate the simple exponential smoothing forecast for the 4th week as follows:
F_1 = D_1 = 50 F_2 = α D_1 + (1-α) F_1 = 0.3 50 + 0.7 50 = 15 + 35 = 50 F_3 = α D_2 + (1-α) F_2 = 0.3 45 + 0.7 50 = 13.5 + 35 = 48.5 F_4 = α D_3 + (1-α) F_3 = 0.3 55 + 0.7 48.5 = 16.5 + 33.95 = 48.2
Therefore, the simple exponential smoothing forecast for the 4th week with α=0.3 is 48.2.