This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: IEOR 162, Spring 2012 Suggested Solution to Homework 03 Problem 1 (Modified from Problems 3.8.11) Note. This is actually NOT a typical blending problem. If you define 12 decision variables, each for a pair of chemical and ingredient, then it is quite possible that the formulation is wrong. Let the decision variables be x i = pounds of chemical i used, i = 1 ,..., 4. Then the data from Table 19 allows us to formulate the three quantity constraints. With the constraint that at least 100 lb of chemical 2 must be used, the complete formulation of this problem is min 8 x 1 + 10 x 2 + 11 x 3 + 14 x 4 s.t. x 1 + x 2 + x 3 + x 4 = 1000 (Total amount produced) . 05 x 1 . 02 x 2 + 0 . 02 x 3 + 0 . 04 x 4 (Quality: ingredient A) . 02 x 1 . 01 x 3 + 0 . 05 x 4 (Quality: ingredient B) . 01 x 1 . 01 x 2 + 0 . 02 x 3 + 0 . 02 x 4 (Quality: ingredient C) x 2 100 (The least amount of chemical 2) x i i = 1 ,..., 4 . In this formulation, the first constraint makes sure that 1000 lb are produced. The three constraints on A, B, and C are then formulated by making the percentage enough. For example, for A it must have . 03 x 1 + 0 . 06 x 2 + 0 . 1 x 3 + 0 . 12 x 4 x 1 + x 2 + x 3 + x 4 . 08 , (1) which is equivalent to . 05 x 1 . 02 x 2 + 0 . 02 x 3 + 0 . 04 x 4 0. As we emphasized in the discussion session, please remove the nonlinear formulations like (1) in your submitted paper . The objective function minimizes the total cost....
View
Full
Document
This note was uploaded on 03/14/2012 for the course IEOR 162 taught by Professor Zhang during the Spring '07 term at University of California, Berkeley.
 Spring '07
 Zhang

Click to edit the document details