1. **State the problem:** We need to forecast this week's production for Monday to Friday using two methods: (i) 4-week simple moving averages and (ii) weighted moving averages with weights 0.50, 0.20, 0.10. 2. **Given data table:** | Week | Monday | Tuesday | Wednesday | Thursday | Friday | |--------------|--------|---------|-----------|----------|--------| | 4 Weeks Before | 320 | 290 | 310 | 260 | 330 | | 3 Weeks Before | 340 | 300 | 320 | 280 | 350 | | 2 Weeks Before | 350 | 310 | 330 | 270 | 340 | | Last Week | 360 | 320 | 340 | 290 | 360 | --- ### (i) 4-week Simple Moving Averages (SMA) 3. SMA is the average of the last 4 weeks for each day. Calculate for Monday: $$\frac{320 + 340 + 350 + 360}{4} = \frac{1370}{4} = 342.5$$ For Tuesday: $$\frac{290 + 300 + 310 + 320}{4} = \frac{1220}{4} = 305$$ For Wednesday: $$\frac{310 + 320 + 330 + 340}{4} = \frac{1300}{4} = 325$$ For Thursday: $$\frac{260 + 280 + 270 + 290}{4} = \frac{1100}{4} = 275$$ For Friday: $$\frac{330 + 350 + 340 + 360}{4} = \frac{1380}{4} = 345$$ --- ### (ii) Weighted Moving Average (WMA) with weights 0.50 (latest week), 0.20, 0.10 (three weeks before) 4. Weights are given as 0.50 for last week, 0.20 for 2 weeks before, 0.10 for 3 weeks before. Since four weeks total are given, we assume the first week's weight is 0. Calculate for Monday: $$0.50 \times 360 + 0.20 \times 350 + 0.10 \times 340 = 180 + 70 + 34 = 284$$ For Tuesday: $$0.50 \times 320 + 0.20 \times 310 + 0.10 \times 300 = 160 + 62 + 30 = 252$$ For Wednesday: $$0.50 \times 340 + 0.20 \times 330 + 0.10 \times 320 = 170 + 66 + 32 = 268$$ For Thursday: $$0.50 \times 290 + 0.20 \times 270 + 0.10 \times 280 = 145 + 54 + 28 = 227$$ For Friday: $$0.50 \times 360 + 0.20 \times 340 + 0.10 \times 350 = 180 + 68 + 35 = 283$$ --- **Final forecast:** | Day | SMA Forecast | WMA Forecast | |-----------|--------------|--------------| | Monday | 342.5 | 284 | | Tuesday | 305 | 252 | | Wednesday | 325 | 268 | | Thursday | 275 | 227 | | Friday | 345 | 283 |