Review problem (Practice set #7, Q6)

A small cruise ship is starting up and trying to decide how much to charge per cabin in order to maximize revenue. It total the cruise ship has 100 cabins. Based on experience they think their demand function will be demand = 100 (price/100) which means they will sell one less cabin for each $100 they raise the price.

1. What price should they set in order to maximize revenue?

b) What is the maximum revenue?

c) How many cabins will they sell at the price that maximizes revenue?

d) It turns out that due to a technical problem 40 cabins are not safe to be used. Should the pricing decision change?

e) Bad luckmore technical problems arise and now 20 more cabins are not safe to be used. Should the pricing decision change?

Practice to price differentiation (practice set #7, Q4)

After designing and producing your brand new case for BacDook Pro 15, your data science team estimates that the demand will be equal to D(p)=1000-10p. You are head of the Operations team and everyone is relying on you for smart pricing!

1. The first and more basic idea would be to set a single price equal. What is the optimal price and how many sales do you expect at that price? What is your optimal revenue?

After remembering what you learned in 311 and the value of price differentiation you come up with the following masterplan. You have your data science team do their machine learning magic and for every potential customer who visits your website you are able to infer their willingness to pay! You will divide your market into two groups, the high willingness to pay to whom you offer a price of $90 and the low willingness to pay to whom you offer a price of $20.

2. How many high willingness to pay customers do you expect have?

3. How much is your new revenue?

4. Is this a good plan?

Thank you!