1. clara's utility function is u(x, y) = (x + 2)(y +1). a) write an equation for clara's indifference curve that goes through the point (x, y) = (2, 8). b) suppose that the price of each good is one and that clara has an income of 11. write an equation that describes her budget constraint. c) find an equation the describes clara's mrs for any given commodity bundle (x, y). d) use the equations in parts b) and c) to solve for clara's optimal bundle( hint use the fact that at clara’s optimal choice = mrs) e) find clara’s demand function for good x (i. e. find x(px, py, m). 2. consider bridget, who has preferences that can be described by the function u(x, y) = 5ln(x) + y. find bridget's demand functions for x and y.

Hye ryung is the president of the local chapter of the american medical students association (amsa). she is organizing local outreach and informational meetings. at her first meeting there are five people present (including herself). every month after that her group grows by 5 people. a. how many members are in the group after 6 months? b. the logistics of hosting and feeding her group at meetings was more complicated than expected. the cost of feeding 5 people at her first meeting was $30, for 10 people it was $35, for 15 it was $45, and after 6 months all of the costs had added up to $100. write a function to model the cost with the number of people attending meetings. c. what connections can you make between the linear growth of the group’s membership and the increasing costs of running meetings?

The vertices of a rectangle are given in the columns of the matrix . if is found to perform a transformation, what are the coordinates of the transformed rectangle? (0, 0), (0, –3), (–3, –3), (–3, 0) (0, 0), (0, 3), (3, 3), (3, 0) (0, 0), (0, 3), (–3, –3), (–3, 0) (0, 0), (0, 3), (–3, 3), (–3, 0)

Josephine has a great garden with and area of 2x2 + x - 6 square feet