Optimization: LP Formulation & Simplex Method Review for OR Midterm Exam 1, Exams of Operational Research

Download Optimization: LP Formulation & Simplex Method Review for OR Midterm Exam 1 and more Exams Operational Research in PDF only on Docsity! IE 335: Operations Research - Optimization Fall 2008 Review Problems for Midterm Exam 1 Problem 1. Priceler manufactures sedans and wagons. The number of each type of vehicle that can be sold in each of the next three months is: Sedans Wagons Month 1 1100 600 Month 2 1500 700 Month 3 1200 500 Each sedan has a profit of $2000, and each wagon has a profit of $1500. To hold a vehicle in inventory from one month to the next costs $150 per sedan and $200 per wagon. During each month, at most 1500 vehicles can be produced. Production line restrictions dictate at least two-thirds of all cars produced during month 1 must be sedans. At the beginning of month 1, 200 sedans and 100 wagons are available. Formulate an LP that can be used to maximize Priceler’s profit during the next three months. Problem 2. Consider the following feasible region: x 2y  4 x y  2 x  0 y  0 a. Graph the feasible region. b. List all the extreme points. If there are none, write “none.” c. Give a maximizing objective function such that .2; 0/ and .0; 0/ are optimal in the feasible region above. d. Give a maximizing objective function such that .2; 2/ is optimal in the feasible region above. e. Add a constraint that makes the feasible region infeasible. Problem 3. Consider the following standard display for the simplex method. Note that some information is missing, and the presence of parameters a; b; c; d; e; f; g. x1 x2 x3 x4 x5 max c a 1 0 b 0 b A 1 1 ? 0 0 9 ? 1 0 1 0 0 1 -2 0 ? 1 0 ::: ::: ::: ::: ::: N N B B B x.t/ 0 0 3 c 1 c
x.t/ D ? x for x1 1 0 d 2 e Nc1 D ? x for x2 0 1 1 f g Nc2 D ? 1