Problem $2($based on the idea of example $15-1)$

A Music store sells compact discs. The supplier manufactures compact discs at $$\frac{1}{?}$ unit and sells it to the music store at $$\frac{5}{?}$ unit. The retailer sells it to the music store at $$\frac{10}{?}$ unit. The market demand is normally distributed with a mean of $1000$ and standard deviation of $300.$

Scenario $1.$ Any leftover is worth less

Scenario $2.$ Any leftover is sold at $$0\mathrm{.}5/$unit

Scenario $3.$ Any leftover is sold at $$2/$unit

a$)$ For scenario $1,$ what will be the optimal order quantity considering a decentralized supply

chain? what will be the optimal order quantity considering a decentralized supply chain?

What will be the difference between maximum profit of centralized and decentralized supply

chain? $($

b$)$ For scenario $2,$ what will be the optimal order quantity considering a decentralized supply chain? what will be the optimal order quantity considering a decentralized supply chain?

What will be the difference between maximum profit of centralized and decentralized supply chain?

c$)$ For scenario $3,$ what will be the issue?

$(Normsinv(0\mathrm{.}5)=0),(Normsinv(0\mathrm{.}53)=0\mathrm{.}066)(Normsinv(0\mathrm{.}95)=1\mathrm{.}62),(Normsinv(0\mathrm{.}9)=1\mathrm{.}28),$