HW1

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School
Northeastern University **We aren't endorsed by this school
Course
OR 6205
Subject
Mathematics
Date
Oct 20, 2023
Pages
2
Uploaded by chiragv96 on coursehero.com
OR 7205 - Fall 2023 Homework 1 Due: Thursday, 21 September 2023, 11:59 PM Instructions: This assignment is to be done individually - you must do your own work. Preliminary Questions (5 Points) 1. (3 Points) Introduce yourself in one paragraph. Tell us about your background, degrees you have, universities you earned those degrees from, the relevant courses you have passed before, the year you were admitted at NU, and anything else you may think might be useful we know you better. 2. (2 Points) Read the syllabus and confirm you have read it completely. Part I. Introduction to Deterministic OR (47 Points) 1. (9 Points) Read the application vignettes on page 25, 54, and 59 of your textbook and summarize them here. 2. (6 Points) Write the parameters and coefficients of the following LP in matrix format. ( P 1) maximize x 1 ,x 2 ,x 3 5 x 1 + 3 x 2 + 2 x 3 subject to: 2 x 1 + x 2 + 4 x 3 4 , - x 1 + x 2 - 2 x 3 1 , x 1 + 3 x 2 + x 3 2 , x 1 , x 2 , x 3 0 . 3. (18 Points) For the following mathematical programming problem identify the LP assumptions that are violated in each line. Justify your answers. ( P 2) minimize x 1 ,x 2 ,x 3 2 x 1 + 3 x 1 x 2 + 3 x 3 subject to: (1) - 4 x 1 + x 2 + 5 x 2 3 7 , (2) x 1 - x 2 + 2 x 3 p , p ∈ { 0 . 4 , 0 . 6 } (3) x 1 /x 3 + 3 x 2 + x 3 3 , (4) x 1 0 , (5) x 2 0 , integer (6) x 3 R . (7)
OR 6205 · Fall 2023 · Homework 1 2 4. (14 Points) Write the following linear program as a minimization problem in standard form. ( P 3) maximize x 1 ,x 2 ,x 3 - 7 x 1 + 2 x 2 - 4 x 3 subject to: 2 x 1 + x 2 + 3 2 x 3 - 3 , - 3 x 1 + 1 3 x 2 - 2 x 3 5 , 2 x 1 + x 2 + 1 4 x 3 = 1 , x 1 R , x 2 0 , x 3 0 . Part II. OR Modeling (48 Points) 5. (8 Points) Answer the question 3.3-2 of the textbook. 6. (15 Points) Answer the problem 3.4-8.(a) of the textbook. 7. (25 Points) Answer the problem 3.4-13.(a) of the textbook.
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