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assignment 2 - MS&E 211 Linear and Nonlinear Optimization...

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MS&E 211 Fall 2007 Linear and Nonlinear Optimization Oct 9, 2007 Prof. Yinyu Ye Homework Assignment 2: Due 3:15pm Thursday, Oct 18 There is a homework collecting box outside of professor Ye’s office (Terman 316) for you to submit your homework. No late homework accepted! Suggested Readings: Chapter 8.1 & 8.2 (Transportation) and Chapter 4.1-4.5 (Simplex method),“Introduction to Operations Research” by Hiller and Lieberman Problem 1: Production Management 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, which sells for $ 38 per barrel, or home heating oil, which sells for $33 per barrel. There are three production processes with the following characteristics: Process 1 Process 2 Process 3 Input crude A 3 1 5 Input crude B 5 1 3 Output gasoline 4 1 3 Output heating oil 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 variable 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 over 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 want to prevent new
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