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IEOR162_hw01 - IEOR 162 Fall 2011 Homework 01 1(Modied from...

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IEOR 162, Fall 2011 Homework 01 1. (Modified from Problem 3.2.3; 10 points) Leary Chemical manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $4 and yields 3 units of A, 1 of B, and 1 of C. Running process 2 for an hour costs $1 and produces 1 unit of A and 1 of B. To meet customer demands, at least 10 units of A, 5 of B, and 3 of C must be produced daily. (a) (4 points) Formulate an LP to determine a daily production plan that minimizes the cost of meeting Leary Chemicals daily demands. (b) (4 points) Graphically solve the LP. (c) (1 points) Write down the binding constraints, if any, at the point (5 , 0). (d) (1 points) Write down the binding constraints, if any, at the point (4 , 3). 2. (Modified from Problem 3.3.2; 10 points) Consider the following LP: max 4 x 1 + x 2 s.t. 8 x 1 + 2 x 2 16 5 x 1 + 2 x 2 12 x 1 0 , x 2 0 . Graphically determine whether it has an unique optimal solution, has multiple optimal solutions, is infeasible, or is unbounded.
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