Your company produces a favorite summertime food product, and you have been placed in charge of forecasting shipments of this product. The historical data below represent your company’s past experience with the product.

Date	Shipments		Date	Shipments
Apr-2014	13,838		Jun-2015	21,056
May-2014	15,137		Jul-2015	13,509
Jun-2014	23,713		Aug-2015	9,729
Jul-2014	17,141		Sep-2015	13,454
Aug-2014	7,107		Oct-2015	13,426
Sep-2014	9,225		Nov-2015	17,792
Oct-2014	10,950		Dec-2015	19,026
Nov-2014	14,752		Jan-2016	9,432
Dec-2014	18,871		Feb-2016	6,356
Jan-2015	11,329		Mar-2016	12,893
Feb-2015	6,555		Apr-2016	19,379
Mar-2015	9,335		May-2016	14,542
Apr-2015	10,845		Jun-2016	18,043
May-2015	15,185		Jul-2016	10,803

a. Since the data appear to have strong seasonality, estimate a Winters’ model using Forecast X. Request the mean absolute percentage error.

b. You also have access to a survey of the potential purchasers of your product. This information has been collected for some time, and it has proved to be quite accurate for predicting shipments in the past.

c. After checking for bias, combine the forecasts in parts (a) and (b), and determine if a combined model may forecast better than either single model based on its MAPE.