As its name suggests, integer linear programming builds on linear programming, which optimizes linear functions over a region defined by linear inequalities. The strength of this technique lies in the highly efficient algorithms available for solving any problem that can be expressed in this form.
An example of linear programming
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Laivo manufactures dairy products on a wholesale scale. Before the annual shutdown, the manager wants to determine how much yogurt and cream to produce in order to maximize the company's profit in euros (€). Each tonne (t) of yogurt sold brings in €500, while each tonne of fresh cream brings in €450. Experience tells the company that it will sell no more than eight tonnes of yogurt, while demand for cream far exceeds its production capacity. Production time is limited to sixty hours: one tonne of yogurt takes six hours to produce, and one tonne of cream takes five. Once produced, the yogurt and cream are kept in a modular storage area with a capacity of fifteen storage units. Each tonne of yogurt requires one unit and each tonne of cream two.
