Big Dairy $($BD$)$ is the largest processor and distributor of fresh milk to local supermarkets, with approximately half of its sales coming from generic supermarket brands. Lux Choc $($LC$)$ is the largest regional producer of high quality, very expensive luxury chocolate. Given their businesses, which firm would you expect to have higher gross margins and which a higher days inventory $($in general takes longer to sell an item$)?$

Higher gross margin: BD Higher days inventory: BD

Higher gross margin: BD Higher days inventory: LC

Higher gross margin: LC Higher days inventory: BD

Higher gross margin: LC Higher days inventory: LC