You have drawn a painting that you want to sell to an anonymous buyer, but you do not know exactly how much they are willing to pay. Based on past experiences, you estimate that the buyer will be willing to pay in monetary units where a random variable is evenly distributed continuously over the interval [200, 500]. Let's assume that your assessment regarding the random variable is correct, i.e., that it is indeed evenly distributed continuously over the interval [200, 500]. What price �p will you choose if you want to maximize your expected profit? What will be your expected profit?

Furniture Forecasting Futura Furniture Products manufactures upscale office furniture for the Office of the Future. The sales division comprises regionally based sales offices made up of sales representatives and regional managers. Sales representativeswho report to the regional managersconduct direct sales efforts with customers in their regions. As part of the sales process, representatives gather information about likely future orders and convey that information back to the regional managers. Regional managers use that information to create sales forecasts, which are then used as the basis for manufacturing schedules. Sales representatives and regional managers are both compensated on a salary plus commission (percentage of revenue as pricing is centrally controlled). However, a regional managers commission is adjusted based on regional sales that exceed the forecasted budget. Corporate managers are concerned with one of Futuras key products, the DeskPod. They worry that DeskPod forecasts are inaccurate, causing extreme havoc in the manufacturing process. How are the forecasts likely to be inaccurate? What do you think is driving this inaccuracy? How might this problem be solved?