Transformations between forms Min vs, max o mince台max-Cx Inequality directions 口ax≥be-axs-b Equalities to inequalities: (ai: row i in matrix A) o ax=b eax> b. and ax s bTransformations between forms ◼ Min vs. max: ❑ min 𝒄 𝑇𝒙 ⇔ max−𝒄 𝑇𝒙 ◼ Inequality directions: ❑ 𝒂𝒊 𝑇𝒙 ≥ 𝑏𝑖 ⇔ −𝒂𝒊 𝑇𝒙 ≤ −𝑏𝑖 ◼ Equalities to inequalities: (𝒂𝒊 : row 𝑖 in matrix 𝐴) ❑ 𝒂𝒊 𝑇𝒙 = 𝑏𝑖 ⇔ 𝒂𝒊 𝑇𝒙 ≥ 𝑏𝑖 , and 𝒂𝒊 𝑇𝒙 ≤ 𝑏𝑖 . 9