It is time for a heating contractor to purchase gas furnaces in preparation for winter. The model they plan to buy costs $600 per unit and sells for $850. Any units left over at the end of the season are expected to be marked down to $500 to clear out inventory. Mean demand is estimated to be for 5,000 units with a standard deviation of 750. The two month supply lead time means only a single order can be placed. How many furnaces should the contractor order, and how much, in dollars, should they expect to lose due to markdowns? The contractor has learned of a different source that can supply the furnace at a cost of $650/unit but that would permit a second order after the start of the sales season. The contractor forecasts that initial demand be for 2,000 snow-blowers with a standard deviation of 400. Based on this information, how many units should the contractor order and how much inventory should be expected from the order?

The contractor ordered from the distributor in question 2, but weather conditions suggest that demand for the remainder of the season will now be for 4,000 furnaces with a standard deviation of 500. How many more units should the contractor purchase, how many are expected to be sold across the entire season, and how many are expected to remain at the end of the season? (Hint: Don’t forget how the first order worked out).