Abstract
Associated with every linear program is another called its dual. The dual of this dual linear program is the original linear program (which is then referred to as the primal linear program). Hence, linear programs come in primal/dual pairs. It turns out that every feasible solution for one of these two linear programs gives a bound on the optimal objective function value for the other. These ideas are important and form a subject called duality theory, which is the topic of this chapter.
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Notes
- 1.
One could take the prices of raw materials as fixed and argue that the value of the final products will fall. It does not really matter which view one adopts, since prices are relative anyway. The point is simply that the difference between the price of the raw materials and the price of the final products must narrow due to this innovation.
References
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Lemke, C. (1954). The dual method of solving the linear programming problem. Naval Research Logistics Quarterly, 1, 36–47.
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Vanderbei, R.J. (2020). Duality Theory. In: Linear Programming. International Series in Operations Research & Management Science, vol 285. Springer, Cham. https://doi.org/10.1007/978-3-030-39415-8_5
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DOI: https://doi.org/10.1007/978-3-030-39415-8_5
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