By Rangarajan K. Sundaram

ISBN-10: 0521497701

ISBN-13: 9780521497701

This publication introduces scholars to optimization conception and its use in economics and allied disciplines. the 1st of its 3 components examines the lifestyles of strategies to optimization difficulties in Rn, and the way those suggestions could be pointed out. the second one half explores how ideas to optimization difficulties switch with adjustments within the underlying parameters, and the final half presents an intensive description of the elemental ideas of finite- and infinite-horizon dynamic programming. A initial bankruptcy and 3 appendices are designed to maintain the e-book mathematically self-contained.

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**Example text**

Shipping costs in dollars per unit are: Destinations 1 2 3 Sources 1 2 8 - 17 21 19 22 The transportation costs from Source 2 to Destination 1 vary. The first 20 units shipped on this route cost $10/unit, and each unit over 20 cost $13/unit. Determine a minimal-cost shipping schedule. 7. Three distribution centers supply four retail stores with a commodity. The supplies at the centers, the demands at the stores, and the shipping costs ($/unit) are as follows: 1 Distribution Centers Retail Stores 2 3 4 Supplies 225 300 375 1 2 3 40 38 35 50 42 54 65 60 55 85 80 76 Demands 200 200 200 200 All 225 units at Center 1 must be shipped.

5C < 300 37? 2. In the above example, the $50 and $60 profit estimates would be determined by subtracting production and delivery costs from the selling price of each of the two boats. Suppose now that the cost to the manufacturer of the 1 ton of aluminum is not fixed. In particular, assume that the price per pound of the last 500 lb of aluminum is 20 cents/lb more than the price of the first 1500 lb, and that the price of the first 1500 lb is the cost used in determining the $50 and $60 profit estimates.

30C < 2000. Similarly, consideration of available machine time and finishing labor leads to the inequalities 67? + 5C < 300 and 37? + 5C < 200 Thus the mathematical problem is to determine 7? and C that maximize the function 507? + 60C and satisfy the constraints 7? > 0, C > 0, 507? + 30C < 2000 67? + 5C < 300 37? 2. In the above example, the $50 and $60 profit estimates would be determined by subtracting production and delivery costs from the selling price of each of the two boats. Suppose now that the cost to the manufacturer of the 1 ton of aluminum is not fixed.

### A First Course in Optimization Theory by Rangarajan K. Sundaram

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Categories: Linear Programming