Question: Sportswear company O'yeah designs and sells wetsuits to the U.S. market. The designs of the wetsuits are updated each year. The process for updating the design typically starts in January the year before the designs are to be released. At this time, the purchasing, design, and sales departments have a two-day meeting to discuss the product portfolio for the upcoming year, including design, functionality, and price. In March, the designs are finalized, and the purchasing department starts negotiating with suppliers across the world.
Production usually starts in September or October the year before the designs are to be released, and lasts until December or January depending on the supplier. In February, retailers start placing their orders to O'yeah, with retail sales of the new designs typically starting in early April.
The season stretches from April to September. As the season progresses, retailers place replenishment orders to O'yeah, who supplies the retailers from a central warehouse. Sales peak in early summer. Towards the end of the summer, sales decline dramatically. When the season ends in September, O'yeah pushes out any remaining inventory to the retailers by offering all models at only 25% of the original selling price.
Part 1: Consider a specific SKU# 001237 (Model A200, size L).
For the upcoming year, O'yeah has negotiated with a supplier to have SKU# 001237 produced and delivered to O'yeah at $175 per unit. SKU# 001237 is sold to retailers at $225, for a unit margin of $50.
Suppose total demand for SKU# 001237 for the upcoming season (the time during which the product is sold at full price) is estimated to follow a Normal distribution with mean 2,500 and standard deviation 400.
How many A200, size L, should O'yeah produce to maximize expected profit? Please round to closest integer.