A hardware store manager is planning purchases of gas furnaces. She has received quotes from two distributors. The first can only deliver prior to the start of the season and charges $1,275/furnace. The second distributor can deliver a first order prior to the start of the season and a second one a few weeks later, charging $1,300/furnace. The manager plans to sell furnaces for $1,450. If there is inventory at the end of winter, furnaces will be sold for $1,250. If the manager were to order in advance for the full season, their plans will be based on expected demand of 400 furnaces with a standard deviation of 60, but if they only need to order initially for early season sales, they will order based on expected demand of 100 furnaces and a standard deviation of 10. 1. How much will the manager expect to pay for furnaces for each of the two distributors? 2. The manager hedged and purchased from the second distributor. Updated forecasts suggest it will be a relatively mild winter, and the manager anticipates expected demand for the rest of the season to be 250 furnaces with a standard deviation of 20. How many more furnaces should the manager order, and what will their expected profit be for the full season? (Hint: Don't forget how the first order worked out)