On November $1,$ Beau, an avid hunter and fisherman, purchased a deep freezer from LMN Appliance Store $($LMN$)$ for $$4,500,$ promising in writing to pay the balance at $$100$ per month and granting to LMN a security interest in the property in terms consistent with and incorporating provisions of the UCC. A financing statement covering the transaction was also properly filled out and signed, and LMN properly filed it on November $30.$ Beau placed the deep freezer in his garage and began storing wild game and fish from his personal expeditions.

After Beau failed to make the December or January payments, LMN went to his home to collect the payments or take the deep freezer. Finding no one home and the garage door wide open, LMN went in and took the deep freezer. Two hours later, Christy, a third party and the present occupant of the house, who had purchased the deep freezer for her own use, stormed into LMN$,$ demanding the return of the deep freezer. She showed LMN a bill of sale from Beau to her, dated December $15,$ that listed the deep freezer and other furnishings in the house.

$($a$)$ What are the rights of LMN$,$ Christy, and Beau? $(5$ points$)$

$($b$)$ Would your answer to part $($a$)$ change if LMN had not filed a financing statement? Why? $(5$ points$)$