线性规划问题（线性规划问题中的决策变量是我们能控制的一些因素）
线性规划问题的标准形式
线性裤缺洞规划的标准形式有：约束条件都是等式；等式约束的右端项为非负的常数；每个变量都要求取非负数值。
线性规划规划模型的表示形式有多种，但为研究分析方便，本教材扮亩确定如下形式为线性规划模型的标准型，其他类型的问题，例如极小化问题，不同形式的约束问题，和有负变量的问题，都可以改写成其等价问题的标准型。
建立数学模型三个步骤：
1、根据影响所要达到目的的因素找到决策变量。
2、由决策变量和所在达到目的之间的函数关系确定目标函数。
3、由决策变量所受的限制条件确定决策变量所要满足的约束条件。
线性规划（Linearprogramming,简称LP）是运筹学中研究较早、发展较快、应用广泛、方法较成熟的一个重要分支，它是辅助人们进行科学管理的一种数学方法。研究线性约束条件下线性目标函数的极值问题的数学理论和方法。英文缩写LP。
它是运筹学的一个重要分支，广泛应用于军事作战胡枯、经济分析、经营管理和工程技术等方面。为合理地利用有限的人力、物力、财力等资源作出的最优决策，提供科学的依据。
线性规划问题
下面是最小费用的两组解,对应的最小费用为1008元:
{{小巴个数,所跑次数,限载人数,费用},{大巴个数,所跑次数,限载人数,费用},{限载总人数,总费用}}
{{3,2,96,288},{4,3,384,720},{480,1008}},
{{2,3,96,288},{4,3,384,720},{480,1008}},
下扮纳颤面是所有满足情况的解(不排除有茄族些重复解):
{{小巴个数,所跑次数,限载人数,费用},{大巴个数,所跑厅败次数,限载人数,费用},{限载总人数,总费用}}
{{6,1,96,288},{4,3,384,720},{480,1008}},
{{2,3,96,288},{4,3,384,720},{480,1008}},
{{2,4,128,384},{4,3,384,720},{512,1104}},
{{2,5,160,480},{4,3,384,720},{544,1200}},
{{3,2,96,288},{4,3,384,720},{480,1008}},
{{3,3,144,432},{4,3,384,720},{528,1152}},
{{3,4,192,576},{3,3,288,540},{480,1116}},
{{3,4,192,576},{4,3,384,720},{576,1296}},
{{3,5,240,720},{3,3,288,540},{528,1260}},
{{3,5,240,720},{4,2,256,480},{496,1200}},
{{4,2,128,384},{4,3,384,720},{512,1104}},
{{4,3,192,576},{3,3,288,540},{480,1116}},
{{4,3,192,576},{4,3,384,720},{576,1296}},
{{4,4,256,768},{3,3,288,540},{544,1308}},
{{4,4,256,768},{4,2,256,480},{512,1248}},
{{4,5,320,960},{2,3,192,360},{512,1320}},
{{4,5,320,960},{3,2,192,360},{512,1320}},
{{4,5,320,960},{4,2,256,480},{576,1440}},
{{5,2,160,480},{4,3,384,720},{544,1200}},
{{5,3,240,720},{3,3,288,540},{528,1260}},
{{5,3,240,720},{4,2,256,480},{496,1200}},
{{5,4,320,960},{2,3,192,360},{512,1320}},
{{5,4,320,960},{3,2,192,360},{512,1320}},
{{5,4,320,960},{4,2,256,480},{576,1440}},
{{5,5,400,1200},{1,3,96,180},{496,1380}},
{{5,5,400,1200},{2,2,128,240},{528,1440}},
{{5,5,400,1200},{3,1,96,180},{496,1380}},
{{5,5,400,1200},{4,1,128,240},{528,1440}},
{{6,1,96,288},{4,3,384,720},{480,1008}},
{{6,2,192,576},{3,3,288,540},{480,1116}},
{{6,2,192,576},{4,3,384,720},{576,1296}},
{{6,3,288,864},{2,3,192,360},{480,1224}},
{{6,3,288,864},{3,2,192,360},{480,1224}},
{{6,3,288,864},{4,2,256,480},{544,1344}},
{{6,4,384,1152},{1,3,96,180},{480,1332}},
{{6,4,384,1152},{2,2,128,240},{512,1392}},
{{6,4,384,1152},{3,1,96,180},{480,1332}},
{{6,4,384,1152},{4,1,128,240},{512,1392}},
{{6,5,480,1440},{0,0,0,0},{480,1440}},
{{6,5,480,1440},{1,0,0,0},{480,1440}},
{{6,5,480,1440},{2,0,0,0},{480,1440}},
{{6,5,480,1440},{3,0,0,0},{480,1440}},
{{6,5,480,1440},{4,0,0,0},{480,1440}},
{{7,1,112,336},{4,3,384,720},{496,1056}},
{{7,2,224,672},{3,3,288,540},{512,1212}},
{{7,2,224,672},{4,2,256,480},{480,1152}},
{{7,3,336,1008},{2,3,192,360},{528,1368}},
{{7,3,336,1008},{3,2,192,360},{528,1368}},
{{7,3,336,1008},{4,2,256,480},{592,1488}},
{{7,4,448,1344},{1,1,32,60},{480,1404}},
{{7,4,448,1344},{2,1,64,120},{512,1464}},
{{7,4,448,1344},{3,1,96,180},{544,1524}},
{{7,4,448,1344},{4,1,128,240},{576,1584}},
{{7,5,560,1680},{0,0,0,0},{560,1680}},
{{7,5,560,1680},{1,0,0,0},{560,1680}},
{{7,5,560,1680},{2,0,0,0},{560,1680}},
{{7,5,560,1680},{3,0,0,0},{560,1680}},
{{7,5,560,1680},{4,0,0,0},{560,1680}}
下面是按照车费由小到大排序的结果:
{{小巴个数,所跑次数,限载人数,费用},{大巴个数,所跑次数,限载人数,费用},{限载总人数,总费用}}
{{3,2,96,288},{4,3,384,720},{480,1008}},
{{2,3,96,288},{4,3,384,720},{480,1008}},
{{7,1,112,336},{4,3,384,720},{496,1056}},
{{4,2,128,384},{4,3,384,720},{512,1104}},
{{2,4,128,384},{4,3,384,720},{512,1104}},
{{6,2,192,576},{3,3,288,540},{480,1116}},
{{4,3,192,576},{3,3,288,540},{480,1116}},
{{3,4,192,576},{3,3,288,540},{480,1116}},
{{7,2,224,672},{4,2,256,480},{480,1152}},
{{3,3,144,432},{4,3,384,720},{528,1152}},
{{5,3,240,720},{4,2,256,480},{496,1200}},
{{5,2,160,480},{4,3,384,720},{544,1200}},
{{3,5,240,720},{4,2,256,480},{496,1200}},
{{2,5,160,480},{4,3,384,720},{544,1200}},
{{7,2,224,672},{3,3,288,540},{512,1212}},
{{6,3,288,864},{3,2,192,360},{480,1224}},
{{6,3,288,864},{2,3,192,360},{480,1224}},
{{4,4,256,768},{4,2,256,480},{512,1248}},
{{5,3,240,720},{3,3,288,540},{528,1260}},
{{3,5,240,720},{3,3,288,540},{528,1260}},
{{6,2,192,576},{4,3,384,720},{576,1296}},
{{4,3,192,576},{4,3,384,720},{576,1296}},
{{3,4,192,576},{4,3,384,720},{576,1296}},
{{4,4,256,768},{3,3,288,540},{544,1308}},
{{5,4,320,960},{3,2,192,360},{512,1320}},
{{5,4,320,960},{2,3,192,360},{512,1320}},
{{4,5,320,960},{3,2,192,360},{512,1320}},
{{4,5,320,960},{2,3,192,360},{512,1320}},
{{6,4,384,1152},{3,1,96,180},{480,1332}},
{{6,4,384,1152},{1,3,96,180},{480,1332}},
{{6,3,288,864},{4,2,256,480},{544,1344}},
{{7,3,336,1008},{3,2,192,360},{528,1368}},
{{7,3,336,1008},{2,3,192,360},{528,1368}},
{{5,5,400,1200},{3,1,96,180},{496,1380}},
{{5,5,400,1200},{1,3,96,180},{496,1380}},
{{6,4,384,1152},{4,1,128,240},{512,1392}},
{{6,4,384,1152},{2,2,128,240},{512,1392}},
{{7,4,448,1344},{1,1,32,60},{480,1404}},
{{6,5,480,1440},{4,0,0,0},{480,1440}},
{{6,5,480,1440},{3,0,0,0},{480,1440}},
{{6,5,480,1440},{2,0,0,0},{480,1440}},
{{6,5,480,1440},{1,0,0,0},{480,1440}},
{{6,5,480,1440},{0,0,0,0},{480,1440}},
{{5,5,400,1200},{4,1,128,240},{528,1440}},
{{5,5,400,1200},{2,2,128,240},{528,1440}},
{{5,4,320,960},{4,2,256,480},{576,1440}},
{{4,5,320,960},{4,2,256,480},{576,1440}},
{{7,4,448,1344},{2,1,64,120},{512,1464}},
{{7,3,336,1008},{4,2,256,480},{592,1488}},
{{7,4,448,1344},{3,1,96,180},{544,1524}},
{{7,4,448,1344},{4,1,128,240},{576,1584}},
{{7,5,560,1680},{4,0,0,0},{560,1680}},
{{7,5,560,1680},{3,0,0,0},{560,1680}},
{{7,5,560,1680},{2,0,0,0},{560,1680}},
{{7,5,560,1680},{1,0,0,0},{560,1680}},
{{7,5,560,1680},{0,0,0,0},{560,1680}}
附上Mathematica 程序,因为程序很小, 所以没有简化程序.没有剔除重复解.
arr = {};
For[m = 0, m = Ceiling[480/16] m = 7, m++,
For[p = 0, p = Ceiling[480/16] p = 5, p++,
For[n = 0, n = Ceiling[480/32] n = 4, n++,
For[q = 0, q = Ceiling[480/32] q = 3, q++,
If[m*p*16 + n*q*32 = 480,
arr =
Append[arr, {{m, p, 16*m*p, 48*m*p}, {n, q, 32*n*q,
60*n*q}, {m*p*16 + n*q*32, 48*m*p + 60*n*q}}];
Break[]
]
]
]
]
]
arr
Sort[arr, #1[[-1]][[-1]] #2[[-1]][[-1]] ]
