$$QUESTIONPerformance Lawn Equipment $($PLE$),$ headquartered in St$.$ Louis, Missouri, is a privately owned designer and producer of traditional lawn mowers used by homeowners. In the past $10$ years, PLE has added another key product, a medium$-$size diesel power lawn tractor with front and rear power takeoffs, Class I three$-$point hitches, four$-$wheel drive, power steering, and full hydraulics. This equipment is built primarily for a niche market consisting of large estates, including golf and country clubs, resorts, private estates, city parks, large commercial complexes, resorts, private estates, city parks, lawn care service providers, etc. PLE provides most of the products to dealerships, which, in turn, sell directly to end users. PLE employs $1,660$ people worldwide. About half the workforce is based in St$.$ Louis; the remainder is split among their manufacturing plants.$$In the United States, the focus of sales is on the eastern seaboard, California, the Southeast, and the south$-$central states, which have the greatest concentration of customers. Outside the United States, PLE$$s sales include a European market, a growing South American market, and developing markets in the Pacific Rim and China. The market is cyclical, but the different products and regions balance some of this, with just less than $30\%$ of total sales in the spring and summer $($in the United States$),$ about $25\%$ in the fall, and about $20\%$ in the winter. Annual sales are approximately $$180$ million.$$ForecastingElizabeth Burke continues to oversee production operations as part of the PLE management team. She is reviewing manufacturing capacity plans for next year and needs good forecasts for sales. She has data for four product families: smaller tractors sold by unit $($homeowners$),$ larger tractors sold to industry, smaller mowers sold by unit, and larger mowers sold to industry. Each set of data is broken up by selling region, with the World column representing the sum of all regions.Elizabeth is interested in forecasting sales of each product family of mowers and tractors in each selling region to assess potential future changes in demands. Graph the data and label your charts appropriately. Consider the trend$-$based forecasting models that we discussed in Chapter $12.$Use the following guidelines when creating forecasts:$$Evaluate potential methods that align with your data.$$ Use the last $18$ months as validation data with trend$-$based models.$$ Optimize parameters in trend$-$based models.$$ When using simple exponential smoothing, set $=0\mathrm{.}05$ and round the actual data for the first month to the nearest hundred to seed your forecast column.$$ For moving averages, use $3$ months$$

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