线性规划问题的标准形式 maximize j=1 subject to ax≤bi for i=1,2,,m j=1 x≥0forj=1,2,..,n maximize cTx subject to Ax ≤b x≥0
线性规划问题的标准形式
mizing a linear function subject to linear constraints,into standard form.A linear program might not be in standard form for any of four possible reasons: 1.The objective function might be a minimization rather than a maximization. 2.There might be variables without nonnegativity constraints. 3.There might be equality constraints,which have an equal sign rather than a less-than-or-equal-to sign. 4.There might be ineguality constraints,but instead of having a less-than-or- equal-to sign,they have a greater-than-or-equal-to sign
minimize -2x1+3x2 subject to x1+ X2 =7 X1- 2x2 4 X1 ≥0 问题4： 为什么说这不是“标准形式”？ 如何将它”转化”为标准形式？
minimize -2x1+3x2 maximize 2x1 3x2 subject to subject to x1+ X2 =7 x1+ X2 =7 x1- 2x2 ≤ 4 x1-2x2 4 xI 0. X1 ≥0 maximize 2x1-3x2+3x2 subject to x1+ x =7 ←☐令X2=X2'-X2 x1-2x 2x2 ≤4 x1.x2.x2 0. 很“无厘 头”？
令x2=x2 ’-x2 ” 很“无厘 头”？
maximize 2x1-3x2+3x subject to x1+3 x2 =7 x1-2x2 2x2 ≤4 X1:X2.X2 0. maximize 2x1 -3x2+3x subject to x1+x2 -x2 ≤7 X1+x2 x ≥7 x1-2x2 2x2 ≤ 4 X1.x2.x2 0 maximize CTX maximize 2x1-3x2+3x3 subject to x1+x2 3≤ > subject to -x1-x2 X3 ≤-7 Ax≤ b 2x1-2x2 +2x3 4 0. x≥ 0. X1,X2,X3