Realizing how popular Chipotle is on the Columbia University campus, Hannah decides to set up a competing burrito stand in the business school, where she sells burritos every day. To test the viability of her business model, she begins by only selling one kind of burrito - a tortilla stuffed with rice. Each tortilla costs her$0.50to procure, and each portion of rice costs her$0.30to produce.

QUESTION 1:

To try to get an estimate of the optimal price, she decides to use dynamic pricing. She starts off with a simple gradient descent scheme, with a constant step-size of0.05times the gradient. She starts at a price of$6, and finds that the demand there is90. She then tries at$6.50, and finds that the demand there is80. Assuming her "current" point is$6, what's the next point her gradient descent algorithm will probe?

A. $7

B. $4.8

C. $7.2

D. $5

QUESTION 2:

Continuing from Question 5, she also tries using Schubert's Algorithm with?=100. She starts with the interval[2,8], and finds that the demands at those two points are100and60respectively. What is the next point she should probe according to Schubert's Algorithm?

A. $5.20

B. $6.56

C. $4.80

D. $3.44

QUESTION 3:

Continuing from Question 6, she realizes after a few months of experimentation that her assumption of a linear price response function is somewhat unrealistic. She believes she now has enough data to put together a robust model of demand. Based on the data she has gathered, she fits the following price-response function: