数学建模作业二：选课策略

1、数学建模作业二：选课策略I选课策略一、问题描述课号课名学分所属类别先修课要求1微积分5数学2线性代数4数学3最优化方法4数学：运筹学微积分：线性代数4数据结构3数学；计算机计算机编程5应用统计4数学；运筹学微积分：线性代数6计算机模拟3计算机：运筹学计算机编程7计算机编程2计算机8预测理论2运筹学应用统计9数学实验3运筹学计算机微积分：线性代数对于上述课程，要求至少选两门数学课、三门运筹学课和两门计算机课。试讨论:（1）为了选修课程门数最少，应学习哪些课程？（2）选修课程最少，且学分尽量多，应学习哪些课程？二、问题分析设xi=l为选修课号f的课程，拓=0不选该门课程。约束条件：（1）最少2门数

2、学课，3门运筹学课，2门计算机课：X1+X2+X3+X4+X52；x+x5+x6+x3+x93；x4+x6+x7+x92o先修课程要求：2x3-xk-x20；2x5-xl-x20；x4-x70:x6-x70；xs-x50:2x9-xl-x2=2,x3+x5+x6+x8+x9=3,x4+x6+x7+x9=2,2x3-x2-x1=0,2x5-x1-x2=0,x4-x7=0,x6-x7=0c8-x5x3r0；x4t0rx5t丄尸x60 x7-1；x81；x9-1故最优解：xl=x2=x3=x6=x7=x9=lz其它为0。所以要使选修课程门数最少，应学习微积分，线性代数，最优化方法，计算机模拟，计算机

3、编程和数学实验，共六门。(2)of利用matheniaticaS中的Maximize()函数，并作如下讨论：(代码)选修课程不超过2门时：Maximize5x1+4x2+4x3+3x4+4x54-3x6+2x7+2x8+3x9,xl=l|xl=0zx2=l|Ix2=0,x2=lI|x2=0,x3=l|x3=0zx4=l|x4=0,x5=l|x5=0zx6=l|Ix6=0zx7=lI|x7=0,x8=l|x8=0zx9=l|x9=0,xl+x2+x3+x4+x5=2,x3+x5+x6+x8+x9=3,x4+x6+x7+x9=2,2x3-x2-xl=0,2x5-xl-x2=0.x4-x7=0.x6

4、x7=0,x8x5=0,2x9-xlx2v=0,xl+x2+x3+x4+x5+x6+x7+x8+x9Indeteriainat-efx3-Indet-erminate9x4-Indeteriainare9x5tIndeterminate,x6-Indeterminate,x7tIndeterminate,x8tIndeterminate,x9tIndeterminate无解；选修课程不超过3门时：Maximize5x1+4x2+4x3+3x4+4x54-3x6+2x7+2x8+3x9,xl=l|xl=0zx2=l|Ix2=0,x2=lI|x2=0,x3=l|x3=0zx4=l|x4=0,x5=

5、l|x5=0zx6=l|Ix6=0zx7=lI|x7=0,x8=l|x8=0zx9=l|x9=0,xl+x2+x3+x4+x5=2,x3+x5+x6+x8+x9=3,x4+x6+x7+x9=2,2x3-x2-xl=0,2x5-xl-x2=0.x4-x7=0,x6x7=0,x8x5Indeterminate,x7tIndeterminate,x8tIndeterminate,x9tIndeterminate无解；数学建模作业二：选课策略I选修课程不超过4门时：Maximize5x1+4x2+4x3+3x4+4x5+3x6+2x7+2x84-3x9,xl=l|xl=Ozx2=l|Ix2=0,x2=

6、l|x2=0,x3=l|x3=0zx4=l|x4=0,x5=l|x5=0zx6=l|x6=0,x7=l|x7=0,x8=l|x8=0zx9=l|x9=0,xl+x2+x3+x4+x5=2,x3+x5+x6+x8+x9=3,x4+x6+x7+x9=2,2x3-x2-xl=0,2x5-xl-x2=0.x4-x7=0.x6x7=0,x8x5=0,2x9x2Indeterminate,x7tIndeterminate,x8tIndeterminate,x9tIndeterminate无解；选修课程不超过5门时：Maximize5x1+4x2+4x3+3x4+4x5+3x6+2x7+2x84-3x9,x

7、l=l|xl=0zx2=l|Ix2=0rx2=lI|x2=0,x3=l|x3=0rx4=l|x4=0,x5=l|x5=0rx6=l|x6=0,x7=l|x7=0,x8=l|x8=0zx9=l|x9=0,xl+x2+x3+x4+x5=2,x3+x5+x6+x8+x9=3,x4+x6+x7+x9=2,2x3-x2-xl=0,2x5-xl-x2=0.x4-x7=0.x6x7=0,x8x5=0,2x9x2Indeteriainat-efx3-Indet-erminate9x4-Indeteriainare9x5tIndeterminate,x6-Indeterminate,x7tIndetermina

8、te,x8tIndeterminate,x9tIndeterminate无解；选修课程不超过6门时：Maximize5x1+4x2+4x3+3x4+4x5+3x6+2x7+2x84-3x9,xl=l|xl=0zx2=l|Ix2=0,x2=l|x2=0,x3=l|x3=0zx4=l|x4=0,x5=l|x5=0zx6=l|x6=0,x7=l|x7=0,x8=l|x8=0zx9=l|x9=0,xl+x2+x3+x4+x5=2,x3+x5+x6+x8+x9=3,x4+x6+x7+x9=2,2x3-x2-xl=0,2x5-xl-x2=0.x4-x7=0.x6x7=0,x8x5=0,2x9x21.xx4

9、0zx51,x6t0J.xx80zx91即选微积分，线性代数，线性代数，最优化方法，应用统计，计算机编程和数学实验这6门课程时，可得学分22分；选修课程不超过7门时：Maximize5x1+4x2+4x3+3x4+4x5+3x6+2x7+2x84-3x9,xl=l|xl=0zx2=l|Ix2=0,x2=l|x2=0,x3=l|x3=0zx4=l|x4=0zx5=l|x5=0zx6=l|x6=0,x7=l|x7=0,x8=l|x8=0zx9=l|x9=0,xl+x2+x3+x4+x5=2,x3+x5+x6+x8+x9=3,x4+x6+x7+x9=2,2x3-x2-xl=0,2x5-xl-x2=0

10、.x4-x7=0.x6x7=0,x8x5=0,2x9x2=0,xl+x2+x3+x4+x5+x6+x7+x8+x90 x9-1ni数学建模作业二：选课策略IV数学建模作业二：选课策略I即选微积分，线性代数，线性代数，最优化方法，应用统计，计算机编程，数学实验和计算机模拟这7门课时，可得学分25分；选修课程不超过8门时：Maximize5x1+4x2+4x3+3x4+4x5+3x6+2x7+2x84-3x9,xl=l|xl=Ozx2=l|Ix2=0zx2=l|x2=0,x3=l|x3=0,x4=l|x4=0,x5=l|x5=0,x6=l|x6=0zx7=l|x7=0,x8=l|x8=0zx9=l|x9=0,xl+x2+x3+x4+x5=2,x3+x5+x6+x8+x9=3,x4+x6+x7+x9=2,2x3-x2-xl=0z2x5-xl-x2=0.x4-x7=0.x6-x7=0zx8x5lrx5-x61.丿x7-lzx80zx9t丄即选修预测理论以外的课程，共8门，可得学分28分；全选时，可得学分31分。综上，要使课程