$2.$ Answer the below questions on lot$-$size and volume$-$based quantity discounts.

i$.$Under what circumstances are lot$-$size$$based and volume$-$based quantity discounts applicable?

ii$.$Consider a toothpaste manufacturer wanting to offer quantity discounts to maximize their profit. Explain whether they should offer lot$-$size$$based or volume$-$based quantity discounts to maximise total supply chain profits.