5‘z{6ˇ"`K Abstract £1⁄ƒ^xK"3z”§5†/˘ 6¶ ? 1 X 0" £2⁄)zKc§K" £3⁄OL§(§=(J(§'" 1 ^X/{)55y£15'⁄ ^I=¶" min x1 − x2 + 2x3 s.t. 2x1 + x2 − x3 ≤ 3, 0 ≤ x1 ≤ 3, − 1 ≤ x2 ≤ 6, x3 ≷ 0. 2 ^X/{)55y£15'⁄ ^I=¶" min 4x1 + 2x2 s.t. 2x1 − 3x2 ≥ 2, − x1 + x2 ≥ 3, xi ≥ 0, ∀i. 1 

3 ^X/{)55y£15'⁄ ^I=¶" min 2x1 − 3x2 + 4x3 s.t. x1 + x2 + x3 ≤ 8, − x1 + 2x2 − x3 ≥ 4, 2x1 − x2 ≤ 6, ∀i. xi ≥ 0, 4 Xe55yØ5y£5'⁄ min − x1 + x2 s.t. 2x1 − x2 ≥ −2, x1 − 2x2 ≤ 2, x1 + x2 ≤ 5, x1 ≥ 0, x2 ≷ 0. 5 ^e{)‘zflK£15'⁄  1 1 1 —': x(1) = min x2 1 + x2 " c 2 gS=§3dL§¥ƒO d(1)! x(2)! d(2)! x(3)§ 2 + 2x2 3 ¿y d(1) d(2) R" 2 

6 ^{)eª‘zflK£10'⁄ .  1 1 —': x(1) = min x2 1 + x2 2 − 4x1 − 5x2 − x1x2 − 5. 7 ^KT^ƒeª‘zflK‘)£15'⁄ 2 − 6x1 − 4x2 1 + x2 min x2 s.t. x1 + x2 ≤ 3, x1, x2 ≥ 0. 8 ^:v…Œ{ƒ)‘zflK£10'⁄ min x2 1 + x2 2 s.t. x1 + x2 = 1. 3