Читать книгу Optimizations and Programming - Bouchaib Radi, Ghias Kharmanda, Michel Ledoux - Страница 40

Consider the problem of an automobile manufacturer that offers two models for sale, a small automobile and a large automobile. Suppose that there is sufficient demand that the manufacturer is certain to sell whatever is produced at the current sales price of 16,000 euros for large automobiles, and 10,000 euros for small ones. The manufacturer’s only problem is the limited supply of two raw materials, rubber and steel. Manufacturing a small automobile requires one unit of rubber and one unit of steel, whereas manufacturing a large automobile requires one unit of rubber and two units of steel. If the manufacturer has 400 units of rubber and 600 units of steel in stock, how many small and large vehicles should be produced from this inventory to maximize the turnover?

Let x be the number of large automobiles manufactured, y the number of small automobiles manufactured and z the resulting turnover. The problem can therefore be expressed in the form:

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