Example $15-1$ Impact of Local Optimization

Consider a music store that sells compact discs. The supplier

manufactures compact discs at $$1$ per unit and sells them to the music

store at $$5$ per unit. The retailer sells each disc to the end consumer at

$$10.$ At this retail price, market demand is normally distributed, with a

mean of $1,000$ and a standard deviation of $300.$ Any leftover discs at the

end of the sale period are worthless. How many discs should an

independent retailer order? What are the supply chain profits with an

independent retailer? If the manufacturer and the retailer are vertically

integrated $($they are a single firm$),$ how many discs should the retailer

order? What are the supply chain profits when the manufacturer and

retailer are a single firm?