An event manager is planning how much coffee to purchase for a research conference. The conference will last for a full day, so to keep the researchers (especially those with severe jetlag!) alert and, perhaps more importantly, to keep the presenters to the point when they speak, coffee is a bare necessity.

While coffee could be bought from any local retailer before or during the conference, the manager wants to place a large order with a wholesaler to reach a more favorable price. Such an order has a lead time of up to five days, so it has to be placed well ahead of the start of the conference.

The wholesaler, whom the manager plans to purchase from, offers ground beans in5 poundbags at $90 per bag. Each bag is estimated to yield 1,500 ounces of brewed coffee. The local retailer offers similar bags at $145 per bag, including immediate delivery to the conference venue. Running out of coffee is not an option, so the manager plans to use as much wholesale coffee as possible and, if it runs out,buylocal retailer coffee for the remaining demand. Unused beans cannot be sold or stored, so if any ground beans remain after the conference they are given away to the crew for free.

When it is time to place the order, registration has closed with 2,000 people registered for the conference. The manager estimates that, on average, each registered participant will drink about 10 ounces of coffee per day. This numberishowever, as you may realize, very uncertain. The manager asks one of his assistants to investigate coffee consumption at previous conferences to provide a more nuanced forecast. After some data mining, the assistant presents the following data (available here).

Part 1

Based on the assistant's forecast, how many bags of coffee beans should be ordered from the wholesaler to minimize expected costs? Answer in integer bags.

unanswered

Part 2

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Following the policy from Part 1, what is the expected loss? Answer in integer dollars. Please enter a positive number.

Part 3

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The wholesaler hears about the event and tells the manager that the wholesaler is willing to buy back any unopened bags of coffee after the conference is over for $75 per bag.

How many bags of coffee beans should be ordered from the wholesaler to minimize expected cost with such a buy back option? Answer in integer bags. unanswered

Part 4

Following the policy from Part 3, what is the expected loss? Round to closest integer dollar. Answer without the dollar symbol. Please enter a positive number.

Part 5

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Independently of whether the manager follows the policy in Part 1 or the policy in Part 3, there is a probability that the manager has to buy some retailer coffee in addition to the coffee from the wholesaler.

Compared to the policy from Part 3, how many more bags should the manager expect to purchase from the local retailer if he uses the policy from Part 1? Answer with two decimals. For instance, if you find that the policy in Part 1 leads to an expected 4.56 bags of retail coffee and the policy in Part 3 leads to an expected 2.31 bags of retail coffee, the solution is 4.56-2.31=2.25 bags of retail coffee, and you answer 2.25.