Answer the following questions in the context of sales and operations planning along the supply chain $($textbook Chapter $9).$

a$)$ Why would a firm want to offer price promotions during its peak demand periods?

b$)$ Why would a firm want to offer price promotions during its low demand periods?

c$)$ What would be the motivation for a supplier and buyer $($business$-$to$-$business$)$ to work together to come up with a mutually agreed price promotion in terms of timing? What is one potential roadblock during such a cooperation?