IE 413 Engineering OR I

♣ ♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ Homework #1

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Part I: Gauss-Jordan Method (3 points) Use the Gauss-Jordan method to determine whether each of the following linear systems has no solution, a unique solution, or an infinite number of solutions. Indicate the solutions (if any exist). Note: Show solution procedures.

(a) 2×2 + 2×3 = 4 x1 + 2×2 + x3 = 4 x2 – x3 = 0

(b) 7×1 + x2 = 2 -x2 + 2×3 = 3 x2 + x3 = 3

Part II: Linear Programming (4 points) Las Cruces 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) Formulate a linear programming model to determine a daily production plan that minimizes the cost of meeting Las Cruces Chemical’s daily demands.

(c) Use the graphical method to find the optimal solution and describe it briefly in “plain English” solve this model. What is your total estimated cost?

Part III. Read Chapter 3.1 (Prototype Example), 3.2 (The Linear Programming Model), and 3.3 (Assumptions of Linear Programming) of the attached, and write a one-page summary report for each section. The summary should be typed, double-spaced with 1″ margins on all sides. Be concise in your writing and consult technical writing references as needed. The body of the summary report should include the sections outlined as follows: (1) Summary of the Chapter’s main point; (2) Your opinion of the Chapters including the most important information you learned (3 points).

2 1 4 4 52 7 2 0 1 5 /0 8 / 2 6 1 2 8. 1 2 3 . 2 4 6. 1 8 7

2 1 4 4 52 7 2 0 1 5 /0 8 / 2 6 1 2 8. 1 2 3 . 2 4 6. 1 8 7

2144527 2015/08/26 128.123.246.187

2144527 2015/08/26 128.123.246.187

2144527 2015/08/26 128.123.246.187

2144527 2015/08/26 128.123.246.187

2144527 2015/08/26 128.123.246.187

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