hw2_2011 - MS&E 211 Fall 2011 Linear and Nonlinear...

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MS&E 211 Fall 2011 Linear and Nonlinear Optimization Oct 11, 2011 Prof. Yinyu Ye Homework Assignmen t 2: Due 6pm Th ursda y , Oct 20 Problem 1: Production Managemen t A manager of an oil refinery has 8 million barrels of crude oil A and 5 million barrels of crude oil B allocated for production during the coming month. These resources can be used to make either gasoline, whic h sells for $ 38 per barrel, or home heating oil, which sells for $33 per barrel. There are three production processes with the following c haracteristics: Process 1 Process 2 Process 3 Input crude A Input crude B Output gasoline Output heating oil 3 1 5 5 1 3 4 1 3 3 1 4 Cost $51 $11 $40 All quantities are in barrels. For example, with the first process, 3 barrels of crude A and 5 barrels of crude B are used to produce 4 barrels of gasoline and 3 barrels of heating oil. The costs in this table refer to v ariable and allocated overhead costs, and there are no separate cost items for the cost of the crudes. (a) First formulate a linear programming problem that would help the manager maximize net revenue o v er the next month. Then use the simplex method to find an optimal solution. Please write down each iteration. (b) Suppose that the selling price of heating oil is sure to remain fixed over the next month, but the selling price of gasoline may rise. Using the simplex tableau, try to decide how high it can go without causing the optimal solution to change. (Hint: You w an t to prev en t new variable from entering the optimal basis while the price is increasing.)
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(c) Now the manager has to consider waste disposal as well. Suppose Process 1 generates 4
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hw2_2011 - MS&E 211 Fall 2011 Linear and Nonlinear...

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