LP in general Max/min a linear function of variables Called the objective function All constraints are linear (in)equalities Equational form: Superscript transpose of vectors. max CTx max C1x1+…+Cnxn s.t. Ax=b s.t. ai1x1+…+ainxn=b Vi=1,…,m x≥0 x1≥0，i=1,.,n x:variables. Inequality:entry-wise (A,b):coefficients in constraints 8LP in general ◼ Max/min a linear function of variables ❑ Called the objective function ◼ All constraints are linear (in)equalities ◼ Equational form: max 𝒄 𝑇𝒙 max 𝑐1𝑥1 + ⋯ + 𝑐𝑛𝑥𝑛 s.t. 𝐴𝒙 = 𝒃 s.t. 𝑎𝑖1𝑥1 + ⋯ + 𝑎𝑖𝑛𝑥𝑛 = 𝑏𝑖 , ∀𝑖 = 1, … , 𝑚 𝒙 ≥ 𝟎 𝑥𝑖 ≥ 0, ∀𝑖 = 1, … ,𝑛 ❑ 𝒙: variables. ❑ (𝐴, 𝒃): coefficients in constraints Superscript T: transpose of vectors. Inequality: entry-wise 8