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Unformatted text preview: MS&E 211 Fall 2010 Linear and Nonlinear Optimization Sep 23, 2010 Caleb Tolman Homework Assignment 1: Due 4:15pm Tuesday, Oct 5, 2010 No late homework accepted! Problem 1 (20pts.) Text book page 28 problem 1. Convert the following problems to standard form. a) Minimize x + 2 y + 3 z subject to 2 ≤ x + y ≤ 3 4 ≤ x + z ≤ 5 x ≥ ,y ≥ ,z ≥ . b) Minimize x + y + z subject to x + 2 y + 3 z = 10 x ≥ 1 ,y ≥ 2 ,z ≥ 1 . Problem 2 (10pts.) Text book page 28 problem 2. A manufacturer wishes to produce an alloy that is, by weight, 30% metal A and 70% metal B. Five alloys are available at various prices as indicated below: Alloy 1 2 3 4 5 % A 10 25 50 75 95 % B 90 75 50 25 5 Price/lb $5 $4 $3 $2 $1.50 The desired alloy will be produced by combining some of the other alloys. The manufacturer wishes to find the amounts of the various alloys needed and to determine the least expensive combination. Formulate this problem as a linear program. Problem 3 (10pts.) Text book page 28 problem 4. A small firm specializes in making five types of spare auText book page 28 problem 4....
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 Linear Programming, Optimization, Convex function, text book page, Caleb Tolman

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