x_{ij}=0

x_{ij}=d_{ij}

d_{ij}=x_{ij}

x_{ij}=0

d_{ij}\geq x_{ij}\geq 0

d_{ij}= x_{ij}

x_{ij}\geq d_{ij}\geq 0

d_{ij}=0

d_{ij}= x_{ij}

d_{ij}\geq x_{ij}\geq 0

x_{ij}\geq d_{ij}\geq 0

d_{ij}=0

\sum_{i\in I_k}\sum_{j=1}^n\, x_{ij}\leq S_k

\sum_{j=1}^n\, x_{ij}> S_k

\sum_{i\in I_k}\sum_{j=1}^n\, x_{ij}\geq S_k

\sum_{i\in I_k}\sum_{j=1}^n\, x_{ij}= S_k

\sum_{i\in I_k}\sum_{j=1}^n\, x_{ij}> S_k

(0;3)

(0;4)

(6.5;0.5)

(4;0)

(1.5;0)

(5.5;0.5)

(2.5;0)

(4;0)

(0;5)

(5;0)

необхідними

достатними

максимальними

мінімальними

f({{x}_{1}},{{x}_{2}},...,{{x}_{n}})={{c}_{1}}{{x}_{1}}+{{c}_{2}}{{x}_{2}}+...+{{c}_{n}}{{x}_{n}}\to \min

\left\{ \begin{matrix}

a_{11}{x}_{1}+{a}_{12}{x}_{2}+...+{{a}_{1n}}{{x}_{n}}\ge {{b}_{1}}, \\

{a}_{21}{{x}_{1}}+{{a}_{22}}{{x}_{2}}+...+{{a}_{2n}}{{x}_{n}}\ge {{b}_{2}}, \\

... \\

{{a}_{m1}}{{x}_{1}}+{{a}_{m2}}{{x}_{2}}+...+{{a}_{mn}}{{x}_{n}}\ge {{b}_{m}}, \\

\end{matrix} \right.

f({{x}_{1}},{{x}_{2}},...,{{x}_{n}})={{c}_{1}}{{x}_{1}^2}+{{c}_{2}}{{x}_{2}^2}+...+{{c}_{n}}{{x}_{n}^2}\to \min

\left\{ \begin{matrix} a_{11}{x}_{1}+{a}_{12}{x}_{2}+...+{{a}_{1n}}{{x}_{n}}\ge {{b}_{1}}, \\ {a}_{21}{{x}_{1}}+{{a}_{22}}{{x}_{2}}+...+{{a}_{2n}}{{x}_{n}}\ge {{b}_{2}}, \\ ... \\ {{a}_{m1}}{{x}_{1}}+{{a}_{m2}}{{x}_{2}}+...+{{a}_{mn}}{{x}_{n}}\ge {{b}_{m}}, \\ \end{matrix} \right.

f({{x}_{1}},{{x}_{2}},...,{{x}_{n}})={{c}_{1}}{{x}_{1}}+{{c}_{2}}{{x}_{2}}+...+{{c}_{n}}{{x}_{n}}\to \min

\left\{ \begin{matrix} a_{11}{x}_{1}+{a}_{12}{x}_{2}+...+{{a}_{1n}}{{x}_{n}}\ge {{b}_{1}}, \\ {a}_{21}{{x}_{1}}+{{a}_{22}}{{x}_{2}}+...+{{a}_{2n}}{{x}_{n}}\ge {{b}_{2}}, \\ ... \\ {{a}_{m1}}{{x}_{1}^2}+{{a}_{m2}}{{x}_{2}^2}+...+{{a}_{mn}}{{x}_{n}^2}\ge {{b}_{m}}, \\ \end{matrix} \right.