{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

midterm 1

# midterm 1 - Economics 172B Introduction to Operations...

This preview shows pages 1–3. Sign up to view the full content.

Economics 172B: Introduction to Operations Research Solutions to Midterm 1: Spring 2009 1. (15 pts) Give a brief explanation for your answer to each part of this question. a. Is f ( x ) = x 2 a concave function, a convex function or neither? ( ) ( ) ' 2 '' 2 0 f x x f x = = > f ( x ) is a convex function. b. Which of the following sets is convex? { x | x 2 16} or { x | x 2 16}. { x | x 2 16} This set is the region of points that make a convex function less than or equal to a constant. (You also could point out that the set includes all the points between –4 and 4.) c. Is f ( x , y ) = – x 4 x 2 + xy – 4 y 2 a concave function, a convex function or neither? 3 2 2 1 2 2 4 2 , 8 12 2 1 1 8 12 2 0 96 15 0 x y f x x y f x y x H D x D x = − + = = = − < = + > f ( x ) is a concave function.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. (15 pts) A , B , C and D are all sets with the general shape shown below. Each specific set may have a different size, position or rotation. a. Clearly illustrate that these sets are not convex. (One illustration is fine.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

midterm 1 - Economics 172B Introduction to Operations...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online