max f( x_{1}, x_{2}, ..., x_{n} ); // Objective function subject to: g_{1}( x_{1}, x_{2}, ..., x_{n} ) = c_{1} // Equality constraints g_{2}( x_{1}, x_{2}, ..., x_{n} ) = c_{2} ... g_{u}( x_{1}, x_{2}, ..., x_{n} ) = c_{u} h_{1}( x_{1}, x_{2}, ..., x_{n} ) ≤ d_{1} // Inequality constraints h_{2}( x_{1}, x_{2}, ..., x_{n} ) ≤ d_{2} ... h_{v}( x_{1}, x_{2}, ..., x_{n} ) ≤ d_{v} 

max a_{1}x_{1} + a_{2}x_{2} + ... + a_{n}x_{n} ; // Objective function subject to: c_{11}x_{1} + c_{12}x_{2} + ... + c_{1n}x_{n} ≤ d_{1} // Constraints c_{21}x_{1} + c_{22}x_{2} + ... + c_{2n}x_{n} ≤ d_{2} .... c_{m1}x_{1} + c_{m2}x_{2} + ... + c_{mn}x_{n} ≤ d_{m} x_{1} ≥ 0, x_{2} ≥ 0, ..., x_{n} ≥ 0 



max: x_{1} + x_{2}
s.t.: x_{1} + 2x_{2} ≤ 8
3x_{1} + 2x_{2} ≤ 12
x_{1} ≥ 0, x_{2} ≥ 0


So an LP is usually written as follows:
max: x_{1} + x_{2} s.t.: x_{1} + 2x_{2} ≤ 8 3x_{1} + 2x_{2} ≤ 12 
The constraints x_{1} ≥ 0, x_{2} ≥ 0 are implicitly assumed !!!
max: x_{1} + x_{2} s.t.: x_{1} + 2x_{2} ≤ 8 3x_{1} + 2x_{2} ≤ 12 





look like this:
max: x_{1} + x_{2} s.t.: x_{1} + 2x_{2} ≤ 8 3x_{1} + 2x_{2} ≤ 12 
Answer:

Graphically:
We can see that:

Important note:
