Читать книгу Optimizations and Programming - Bouchaib Radi, Ghias Kharmanda, Michel Ledoux - Страница 14

 – The function cT x is the objective function, cost function or loss function.

 – The components of the vector x are called decision variables.

 – If the vector x satisfies all constraints, then x is an admissible solution.

 – The set of all admissible solutions is the admissible set or admissible region.

 – An admissible solution x* that maximizes the loss function (i.e. cTx* ≥ cTx for every admissible x) is called an optimal admissible solution or optimal solution.

EXAMPLE 1.1.– A factory manufactures two products P₁ and P₂ while consuming certain resources: equipment, labor and raw materials. The needs are listed in the following table. Each resource is available in limited quantities.

	P 1	P 2	Availability
Equipment	3	9	81
Labor	4	5	55
Raw materials	2	1	20

The two products P₁ and P₂ yield effective profits of 6 dhs and 4 dhs per unit. The goal is to determine which (possibly non-integer) quantities of the products P₁ and P₂ the factory should produce to maximize the total profit from selling these two products, subject to the availability of the resources.

Let x₁ and x₂ be the quantities of the products P₁ and P₂, respectively.

The LP may be expressed as follows: maximize z(x₁, x₂) = 6x₁ + 4x₂ subject to:

 – availability of resources:

 – positivity of variables: x1, x2 ≥ 0