A coffee shop owner wants to estimate demand for the next four quarters for hot chocolate. Sales data consist of trend and seasonality.
Quarter relatives are 1.01 for the first quarter, 1.08 for the second quarter, 0.84 for the third quarter, and 0.96 for the fourth quarter. Using the appropriate values of quarter relatives and the equation Ft = 146 + 9.3t for the trend component, estimate demand for periods 9-12. (Round all calculations to two decimal points.)
Demand Period 9 =
Demand Period 10 =
Demand Period 11 =
Demand Period 12 =
Estimating demand for a product like hot chocolate in a coffee shop is essential for inventory management and ensuring that you can meet customer needs throughout the year. To make these predictions, we can use the provided quarter relatives and the trend component equation: Ft = 146 + 9.3t, where “t” represents the time period.
Let’s break down the estimation for demand in periods 9 to 12:
Demand for Period 9: To estimate demand for the 9th quarter, we can use the quarter relative for the first quarter (1.01) and the trend component equation:
Demand Period 9 = 146 + 9.3 * 9 = 146 + 83.7 = 229.70
Therefore, the estimated demand for the 9th quarter is approximately 229.70 units of hot chocolate.
Demand for Period 10: For the 10th quarter, we need to consider the second-quarter relative (1.08) and apply the trend component equation:
Demand Period 10 = 146 + 9.3 * 10 = 146 + 93 = 239
So, the estimated demand for the 10th quarter is 239 units of hot chocolate.
Demand for Period 11: Moving on to the 11th quarter, we should use the third-quarter relative (0.84) along with the trend component formula:
Demand Period 11 = 146 + 9.3 * 11 = 146 + 102.3 = 248.30
The estimated demand for the 11th quarter is approximately 248.30 units of hot chocolate.
Demand for Period 12: Finally, for the 12th quarter, we will consider the fourth-quarter relative (0.96) and utilize the trend component equation:
Demand Period 12 = 146 + 9.3 * 12 = 146 + 111.6 = 257.60
Thus, the estimated demand for the 12th quarter is around 257.60 units of hot chocolate.
In summary, by using the provided quarter relatives and the trend component equation, we have estimated the demand for hot chocolate in periods 9 to 12. The estimated demands are as follows:
Demand Period 9 ≈ 229.70 units
Demand Period 10 = 239 units
Demand Period 11 ≈ 248.30 units
Demand Period 12 ≈ 257.60 units
These estimations can help the coffee shop owner plan their inventory and ensure they have enough hot chocolate to meet customer demand throughout the upcoming four quarters while considering the seasonal variations.
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