HW3 (1)

IOE 310 – Optimization and Computational Methods (Fall 2023) Homework № 3 Problem 1 (5 points) What are you passionate about? Problem 2 (5 points) (You will have one question like this in almost every homework assignment to ensure that everyone fully reads the Syllabus.) What programming language will we be using in this course? Have you used this language before? Problem 3 (10 points) Consider the following optimization problem in standard form: min x 3 x 1 - 4 x 2 + 7 x 3 s.t. x 1 + 2 x 2 - 3 x 3 = 7 x 1 + x 3 = 4 x 1 , x 2 , x 3 ≥ 0 . Write out the vector c , the vector b , the vector x vector, and the matrix A . Problem 4 (20 points) Convert the following linear programs into standard form. (a) min x x 1 + x 2 s.t. x 1 + 2 x 2 ≤ - 7 x 1 - x 2 ≥ - 2 (b) max x 4 x 1 + 2 x 2 - 177 x 3 s.t. x 1 - 2 x 2 ≤ - 4 2 . 5 x 1 - x 3 = 7 x 1 + x 2 + x 3 ≥ - 4 x 1 ≤ 7 x 1 ≥ 0 , x 3 ≤ 0 Problem 5 (30 points) Briarwood Mall in Ann Arbor is considering a major restructure, and management is considering which stores the mall should include. The total amount of space available for the mall is 29,000 square feet. Management has decided on the following restrictions: • no more than 25% of the space in the mall must be dedicated to stores that serve food and drink; • at least 50% of the space must be dedicated to stores that sell clothes; • have at least 1,500 square feet dedicated to stores that sell books; • at least 20% of the space dedicated to stores that sell electronics; • at least 35% of the space dedicated to stores primarily for kids. IOE Department – University of Michigan Page 2 / 3