Читать книгу Optimizations and Programming - Bouchaib Radi, Ghias Kharmanda, Michel Ledoux - Страница 43

Suppose now that the automobile manufacturer has a competitor who offers to repurchase all raw materials in stock to fulfill a large number of orders. The competitor must offer a certain price (assumed to be constant and denoted u) per unit of rubber and another price (denoted v) per unit of steel. For the offer to be accepted, the price paid by the competitor must at least be equal to the turnover that the manufacturer could achieve by manufacturing automobiles itself. The competitor’s problem can therefore be written as

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Graphical analysis finds the optimal solution u = 4, 000 and v = 6, 000, which corresponds to a global price of p = 5, 200, 000. Observe (and we will see later that this is no coincidence) that the optimal solution of the competitor’s problem (the dual problem to the manufacturer’s primal problem) coincides with the marginal prices of the manufacturer’s problem, and the minimum price that the competitor can offer is equal to the manufacturer’s maximum turnover.