Hotel Fancyname is starting to take bookings for Thanksgiving 2022, which is now 100 days away. The hotel has a capacity of 150 rooms. Customers can choose one of the following offerings for their stay.

Three nights stay beginning Thursday, checking out on Sunday (Thursday, Friday, and Sat nights) for $120 per night.

One night stay on either Thursday, Friday, or Saturday night for $150 per night

Two nights stay beginning Thursday (Thursday and Friday nights) or beginning Friday (Friday and Saturday nights) for $130 per night.

On each day, a customer request for a three-night stay arrives with a probability of 0.25, for each of the one-night stays arrives with a probability of 0.1, and for each of the two-night stays arrives with a probability of 0.2 (for a total probability of customer request arrival of 0.25 + 0.1 x 3 + 0.2 x 2 = 0.95).

We will model the problem of managing customer booking requests as a network revenue management problem. Answer the following questions:

(4 points) Identify the products and the resources in this setup.

(2 points) Calculate the expected demand for each product over the next 100 days.

(8 points) Under the fluid approximation, write a linear program to compute the value of the 150 rooms for the three nights of the Thanksgiving weekend over the next 100 days.

(8 points) Under the fluid approximation, write the dual of the above linear program to compute the current shadow prices of the resources.

(8 points) Solve the above dual linear program in ipython (take a snapshot of your ipython code and attach it to your submission file). Based on the computed shadow prices, compute the bid price for each product.