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Answer :
The seasonal index for Week 1 is approximately 0.410, Week 2 is 0.933, Week 3 is 1.032, and Week 4 is 1.623. Forecasted sales for Week 4, with 50,000 blue jeans forecasted for the next month, would be approximately 81,150 blue jeans.
To calculate the seasonal indices for each week of the month, we need to find the average sales for each week and then divide it by the total average sales for all weeks. Let's calculate the seasonal indices:
Week 1: The sales for Week 1 are given as 6,200 blue jeans. Since there are four weeks in a month, the average sales for Week 1 would be 6,200 divided by 4, which is 1,550 blue jeans.
Week 2: The sales for Week 2 are given as 14,100 blue jeans. The average sales for Week 2 would be 14,100 divided by 4, which is 3,525 blue jeans.
Week 3: The sales for Week 3 are given as 15,600 blue jeans. The average sales for Week 3 would be 15,600 divided by 4, which is 3,900 blue jeans.
Week 4: The sales for Week 4 are given as 24,500 blue jeans. The average sales for Week 4 would be 24,500 divided by 4, which is 6,125 blue jeans.
To find the total average sales, we sum up the average sales for all four weeks and divide by 4:
Total average sales = (1,550 + 3,525 + 3,900 + 6,125) / 4 = 15,100 / 4 = 3,775 blue jeans.
Now, let's calculate the seasonal indices for each week:
Week 1: Seasonal index = Average sales for Week 1 / Total average sales = 1,550 / 3,775 ≈ 0.410 or 41.0%
Week 2: Seasonal index = Average sales for Week 2 / Total average sales = 3,525 / 3,775 ≈ 0.933 or 93.3%
Week 3: Seasonal index = Average sales for Week 3 / Total average sales = 3,900 / 3,775 ≈ 1.032 or 103.2%
Week 4: Seasonal index = Average sales for Week 4 / Total average sales = 6,125 / 3,775 ≈ 1.623 or 162.3%
To forecast the sales for Week 4 when 50,000 blue jeans are forecasted for the next month, we multiply the total forecasted sales by the seasonal index for Week 4:
Forecasted sales for Week 4 = 50,000 * 1.623 ≈ 81,150 blue jeans.
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