midterm 1

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

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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 xx fx = => 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 42 , 8 12 2 1 18 12 2 0 96 15 0 xy f y f x y x H Dx =− + = − ⎡⎤ −− = ⎢⎥ ⎣⎦ − < =+ > f ( x ) is a concave function.
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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.
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This note was uploaded on 06/08/2010 for the course ECON 171 taught by Professor Newhouse during the Spring '07 term at UCSD.

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

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