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 $10\mathrm{.}1.$ 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: Dont forget how the first order worked out$).$