Festive Floral is gearing up for online carnation sales thisMother’s Day. They specialize in selling organic extra-large redand pink carnations. The price is $0.7 per stem, which includesfree one-day shipping to the customer.

Festive Floral pre-orders carnations directly from a certifiedorganic farm at the cost of $0.15 per stem. The order is made priorto the growing season and flowers are grown accordingly, so thepre-order quantity cannot be changed. However, if Festive Floralruns out of pre-ordered carnations, they can always pick up moreimmediately from a local wholesaler that carries carnations of thesame quality, at the price of $0.5 per stem.

Historical demand for the past 10 years are given below, andalso in the attached spreadsheet. Year	Red	Pink
2008	4008	3288
2009	3948	3648
2010	4092	3636
2011	3984	3684
2012	3996	3792
2013	3888	3720
2014	4128	3564
2015	4104	3744
2016	4380	3828
2017	4392	3744

(a) (5 points) Using exponential smoothing with parameter ?? =0.9, what is your forecast for red carnations in 2018? What is theMAD of your forecast?

(b) (3 points) Based on the forecast above, what is the optimalnumber of red carnations to pre-order from the farm?

(c) (8 points) Repeat Parts (a) and (b) for pink carnations.

The carnations are sold in dozens, and each dozen comes with adesigner gift tag that says “Happy Mother’s Day 2018 from FestiveFloral!” The gift tags are identical for carnations of bothcolors.

(d) (5 points) Using exponential smoothing with parameter ?? =0.9, what is your forecast for gift tags? What is the MAD of yourforecast?

(e) (5 points) Using the same z-value as for carnations, what isthe optimal number of gift tags to prepare? Is this more or lessthan the total dozens of carnations, and why?

(f) (4 points) Experiment with the exponential smoothingparameter ?? for the forecast of gift tags in part (d). What is thevalue of ?? that minimizes the MAD?