Using a three period moving average, we can find the forecast for period 4 by taking the average of periods 1, 2, and 3, and then moving the window forward to periods 2, 3, and 4, and so on. Therefore, the forecast for period 4 would be:
(10,000 + 12,400 + 13,250) / 3 = 11,883.33
So, the closest answer is (c) 11,883.
For the second question:
Using a four period weighted moving average, we can find the forecast for period 5 by taking a weighted average of the four most recent periods, where the weights are 0.05, 0.15, 0.30, and 0.50 for the oldest to the most recent periods, respectively. Therefore, the forecast for period 5 would be:
(0.05 x 10,000) + (0.15 x 12,400) + (0.30 x 13,250) + (0.50 x 14,750) = 13,105
So, the closest answer is (a) 13,105.