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? Please explain step by step.