Management of the ABC Floral Shop feels that its sales are seasonal in nature with a monthly seasonal pattern and no trend. The demand data and seasonal ratios for the past three years are given as follows.

a. Calculate a forecast for the past year using A0 = 15,000, α = γ = .3, and the seasonal ratios shown above. For each period, calculate the forecast and the updated seasonal ratio.
b. Plot the original data and the forecast on a graph.
c. Calculate the tracking signals for the past year using MAD0 = 0. Are they within tolerances?
d. Using the classical decomposition method described in the chapter supplement, calculate the seasonal ratios from the data and determine the trend and average levels. Use these ratios and estimates of trend and level to make a forecast for the next year.

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Year 1 Year 2 Year 3 Seasonal Month Demand Demand Demand Jan Mar. Ratio $12,400 11,800 $13,600 0.8 1.8 0.9 1.6 2.0 23,000 24,11 15,800 20,500 25,100 16,200 12,000 10,300 11,800 14,000 10,700 7,600 16,500 14,900 21,000 19,400 24,300 26,000 15,800 16,500 11,500 12,400 10,100 10,800 11,000 12,500 14,300 13,800 10,900 10,600 8,100 May June July Aug 0.7 0.6 0.7 0.9 0.6 Dec. 7,200