fundamental-engineering-optimization-methods.pdf

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Download free eBooks at bookboon.com Fundamental Engineering Optimization Methods 89 Linear Programming Methods c) If the yield/acre for tomatoes increases by 10%, how is the optimum affected? The answer is found by re-computing the reduced costs as: ൌ ࢟ ࡭ െ ࢉ ൌ ሾെͲǤͳͷǡ ʹǡ Ͳሿ ² Since a reduced cost is now negative, additional Simplex steps are needed to regain optimality. This is done and the new optimum is: ݔ כ ൌ ͺ͵Ǥ͵͵ǡ ݔ כ ൌ Ͳǡ ݔ כ ൌ Ͳ ZLWK ݖ כ ൌ ͶͳʹǤͷ ² d) If the yield/acre for cucumbers drops by 10%, how is the optimum be affected? The answer is found by re-computing the reduced costs as: ൌ ࢟ ࡭ െ ࢉ ൌ ሾͲǤ͵ǡ ʹǡ ͲǤͶሿ ² The reduced costs are non-negative, but is no more a basic variable. Regaining the basis results in reduced cost for becoming negative. Additional Simplex steps are performed to regain optimality, and the new optimum is: ݔ כ ൌ ͺ͵Ǥ͵͵ǡ ݔ כ ൌ Ͳǡ ݔ כ ൌ Ͳ ZLWK ݖ כ ൌ ͵͹ͷ ² e) If the man-hours needed to grow green peppers increase to 5/acre, how is the optimum affected? The answer is found by re-computing the reduced cost: ܿ Ƹ ൌ ݕ ܣ െ ܿ ൌ ͲǤͶ ² Since ݔ Z was non-basic and the revised reduced cost is non-negative, there is no change in the optimum solution. 5.5 Duality Theory for the LP Problems In this section we extend the Lagrangian duality (Sec. 4.5) to the LP problems. Duality theory applies to practical LP problems in engineering and economics. In engineering, for example, the primal problem in electric circuit theory may be posed in terms of electric potential, and its dual in terms of current flow.
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• Winter '17
• sam

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