1. I operate a tour company that offers private weekend tours of the city. Each private tour lasts the entire weekend and is operated by a dedicated tour guide. There is a single price for each tour no matter how many people are participating in the tour.

The upcoming Memorial Day weekend is always a busy weekend for my business. From past years' data, I estimate that demand for my tours will follow the demand function,

D(p) = 300 - 0.2p,

where D(p) is the number of tours I will sell if I charge price p per tour. For each tour, I pay the tour guide $150 as well as incur an extra $200 in other operating costs.

1. If I want to maximize my expected profit, what price should I charge for each tour? 

2. What is my revenue under the profit-maximizing price from part a)? 

3. If only 105 guides are available to work on Memorial Day weekend, does my profit-maximizing price change? If it does, what is the new profit-maximizing price? 

4. I have asked all my guides to get back to me by the end of the week about whether they can work on Memorial Day weekend. Once I know the exact number of guides who will be available to work, I will set the profit-maximizing price and begin advertising this price to customers. From historical data, I believe the number of guides who will be available to work on Memorial Day weekend follows the discrete distribution below:

Tour guides are only paid if they give a tour.

Given this distribution, what is my expected profit for Memorial Day weekend? 

5. Assume from now on that I have decided to price my tours at $950 each. As a result, I expect to sell 110 tours and my profit will be $66,000.

I am still waiting to hear back from my normally employed tour guides, and I believe the number of guides who will be available to work on Memorial Day weekend follows the discrete distribution from part d). If not enough of my normal tour guides are available to work on Memorial Day weekend, I will be forced to turn away customers. Note that if I only sell 105 tours and I charge $950 for each tour, my profit will be $63,000.

I can hire 5 new temporary tour guides just for Memorial Day weekend, but I need to decide whether I will hire them before I hear back from my normal guides’ availabilities. If I hire these temporary tour guides, I must pay them an upfront, non-refundable fee per tour guide in addition to the normal $150 per tour. What is the maximum amount of upfront fee per temporary tour guide I should be willing to pay? 

6. Suppose the fee is not paid upfront, and I only pay the extra fee if I use these temporary tour guides. What is the maximum fee I should be willing to pay each temporary tour guide? 

Q (# of guides)	105	115	125	135
Probability that exactly Q guides are available to work on Memorial Day weekend	0.3	0.3	0.2	0.2

Answer rating: 100% (QA)

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