Sample problem

Retailer of an expensive winter jacket purchases them from a manufacturer by placing a single order before the start of the selling season.

The retail and wholesale prices of the jacket are $$125$ and $$80,$ respectively, whereas its production cost to the manufacturer $($unknown to the retailer$)$ is $$35.$

The manufacturer also has a fixed cost to produce each batch of jackets of $$100,000.$ Assume the demand of the jackets is uniformly distributed between $8,000$ and $16,000,$ and the retailer can sell the unsold jackets to a discounter for $$20$ each.