Operations Management: Sustainability and Supply Chain Management (12th Edition)
Operations Management: Sustainability and Supply Chain Management (12th Edition)
12th Edition
ISBN: 9780134130422
Author: Jay Heizer, Barry Render, Chuck Munson
Publisher: PEARSON
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Chapter B, Problem 4P

B.4. Consider the following linear programming problem:

Maximize Pr ofit = 30 X 1 + 10 X 2 Subject to : 3 X 1 + X 2 300 X 1 + X 2 200 X 1 100 X 2 50 X 1 X 2 0 X 1 , X 2 0

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1. For each statement specify whether it is True or False? MLP solver is a heuristic method. A local optimum is better than all nearby points. An optimization problem can only have one local optimal solution. A global optimum is the best point in the entire feasible region. An optimization problem can only have one global optimal solution. For linear optimization problems any local optimal solution is a global optimal solution. For some nonlinear programming problems, Solver can get stuck at a local optimum and never find the global optimum. Forsomelinearprogrammingproblems,Solvercangetstuckatalocaloptimumandnever find the global optimum. Solver is guaranteed to find the global optimum for convex nonlinear optimization problems. A heuristic is a relatively simple solution method that often provides good but not necessarily optimal solutions. MLP solver is a heuristic method.
68. Based on Westerberg, Bjorklund, and Hultman (1977). Newcor’s steel mill has received an order for 25 tons of steel. The steel must be 5% carbon and 6% molybdenum by weight. The steel is manufactured by combining three types of metal: steel ingots, scrap steel, and alloys. Four individual steel ingots are available. At most, one of each can be purchased. The weight (in tons), cost per ton, and the carbon and molybdenum content of each ingot are given in the cells filled in light blue. Three types of alloys can be purchased. The cost per ton and chemical makeup of each alloy are given in the same file. Steel scrap can be purchased at a cost of $100 per ton. Steel scrap contains 3% carbon and 9% molybdenum. Determine how Newcor can minimize the cost of filling its order.
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