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IEOR162_hw04

# IEOR162_hw04 - IEOR 162 Spring 2010 Suggested Solution to...

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IEOR 162, Spring 2010 Suggested Solution to Homework 04 Problem 3.8.7 Let the decision variables be x ij = oz of chemical i used for producing drug j , i = 1 , 2, j = 1 , 2. Also we define the following parameters: P j is the sales price of one oz of drug j , C i is the purchasing cost of one oz of chemical i , S i is the total amount of supply of chemical i (in oz), and D j is the demand size of drug j (in oz). Specifically, we have P = £ 6 5 / , C = 6 4 , S = 45 40 , D = £ 40 30 / . With the definitions of variables and parameters, we formulate the problem as max 2 X j =1 P j 2 X i =1 x ij - 2 X i =1 C i 2 X j =1 x ij s.t. 2 X i =1 x ij D j j = 1 , 2 2 X j =1 x ij S i i = 1 , 2 0 . 3 x 11 - 0 . 7 x 21 0 , - 0 . 6 x 12 + 0 . 4 x 22 0 x ij 0 i = 1 , 2 , j = 1 , 2 . The objective function consists of two parts, the sales revenue and the purchasing cost. The first constraint ensures that the total sales of each drug point is at most the demand size. The second constraint ensures that the total usage of each chemical does not excess the supply quantity. The third constraint ensures the quality. The last constraint is the nonnegativity constraint. Problem 3.8.11 Note that 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.

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