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matlab source code:

% Ex3_3.m% Example 3.3%  Optimization Using MATLAB by P.Venkataraman%%	Using drawLine.m %drawLine(0,6,1,1,5,'l');drawLine(0,6,2,1,4,'e');drawLine(0,6,1,1,1,'g');drawLine(0,6,2,-1,8,'n');xlabel('Hours spent studying');ylabel('Hours of pin ball');title('Example 3.3 -Equality Constraint and Negative Design Variables')grid

% drawLine.m% Drawing linear constraints for LP programming problems% Dr. P.Venkataraman% Optimization Using Matlab% Chapter 3 - linear Programming%% Lines are represented as: ax + by = c ( c >= 0)% x1, x2 indicate the range of x for the line% typ indicates type of line being drawn l (<=)%                                        g, (>=)%                                        n  (none)%% The function will draw line(s) in the figure window% the green line represents the actual value % of the constraint% the red dashed line is 10 % larger or smaller% (in lieu of hash marks)% the limit constraints are identifies in magenta color% the objective function is in blue dashed lines%function ret = drawLine(x1,x2,a,b,c,typ)% recognize the types and set colorif (typ == 'n')    str1 = 'b';   str2 = 'b';   cmult = 1;elseif (typ == 'e')      str1 ='m';      str2 ='m'; else   str1 = 'g';   str2 = 'r';end% values for drawing hash marks% depending on the direction of inequalityif (typ ~= 'n' | 'e')    if (typ == 'l')      cmult = +1;   else cmult = -1;   endend% set up a factor for drawing the hash constraintif (abs(c) >= 10)   cfac = 0.025;elseif (abs(c)> 5) & (abs(c) <  10)   cfac = 0.05;else   cfac = 0.1;endif (c == 0 )    cdum = cmult*0.1; else   cdum = (1 + cmult* cfac)*c;end% if b = 0 then determine end points of line x lineif ( b ~= 0)   y1 = (c - a*x1)/b;   y1n = (cdum - a* x1)/b;   y2 = (c - a* x2)/b;   y2n = (cdum - a*x2)/b;else   % identfy limit constraints by magenta color   str1 = 'm';   str2 = 'm';   y1 = x1; % set  y1 same length as input x1   y2 = x2;  % set y2 same length as input x2   x1 = c/a;  % adjust x1 to actual value   x2 = c/a;  % adjust x2 to actual value   y1n = 0;  % set y = 0;   y2n = 0;  % set  y = 0endif (a == 0)    str1 = 'm'; % set color for limit line   str2 = 'm'; % set color for limit lineend;% draw axis with solid black colorhh = line([x1,x2],[0,0]);set(hh,'LineWidth',1,'Color','k');hv = line([0,0],[x1,x2]);set(hv,'LineWidth',1,'Color','k');% start drawing the linesh1 = line([x1 x2], [y1,y2]);if (typ == 'n')    set(h1,'LineWidth',2,'LineStyle','--','Color',str1);else   set(h1,'LineWidth',1,'LineStyle','-','Color',str1);endif (b ~= 0)&(a ~= 0)   text(x1,y1,num2str(c));endif( b == 0)|(a == 0)| (typ == 'n') | (typ == 'e')   grid   ret = [h1];   return, end grid;h2 = line([x1 x2], [y1n,y2n]);set(h2,'LineWidth',0.5,'LineStyle',':','Color',str2);gridhold onret = [h1 h2];

here, I would like to analysis drawLine.m

% drawLine.m

% Drawing linear constraints for LP programming problems % Dr. P.Venkataraman % Optimization Using Matlab % Chapter 3 - linear Programming % % Lines are represented as: ax + by = c ( c >= 0) % x1, x2 indicate the range of x for the line % typ indicates type of line being drawn l (<=) %                                        g, (>=) %                                        n  (none) % % The function will draw line(s) in the figure window % the green line represents the actual value  % of the constraint % the red dashed line is 10 % larger or smaller % (in lieu of hash marks) % the limit constraints are identifies in magenta color % the objective function is in blue dashed lines % function ret = drawLine(x1,x2,a,b,c,typ) % recognize the types and set color if (typ == 'n')     str1 = 'b';    str2 = 'b';    cmult = 1; elseif (typ == 'e')       str1 ='m';       str2 ='m';  else    str1 = 'g';    str2 = 'r'; end

str1是第一根线的颜色,str2是第二根线的颜色 % values for drawing hash marks % depending on the direction of inequality if (typ ~= 'n' | 'e')     if (typ == 'l')       cmult = +1;    else cmult = -1;    end end 确定第二根线的挪动方向 % set up a factor for drawing the hash constraint if (abs(c) >= 10)    cfac = 0.025; elseif (abs(c)> 5) & (abs(c) <  10)    cfac = 0.05; else    cfac = 0.1; end if (c == 0 )     cdum = cmult*0.1;  else    cdum = (1 + cmult* cfac)*c; end 确定挪动的距离 % if b = 0 then determine end points of line x line if ( b ~= 0)    y1 = (c - a*x1)/b;    y1n = (cdum - a* x1)/b;    y2 = (c - a* x2)/b;    y2n = (cdum - a*x2)/b;

确定第一根线和第二根线的方程

h1 = line([x1 x2], [y1,y2]);  [x1 x2]为x的范围, [y1,y2]为y的范围

h2 = line([x1 x2], [y1n,y2n]);

else    % identfy limit constraints by magenta color    str1 = 'm';    str2 = 'm';    y1 = x1; % set  y1 same length as input x1    y2 = x2;  % set y2 same length as input x2    x1 = c/a;  % adjust x1 to actual value    x2 = c/a;  % adjust x2 to actual value    y1n = 0;  % set y = 0;    y2n = 0;  % set  y = 0

当线垂直的情况

end if (a == 0)     str1 = 'm'; % set color for limit line    str2 = 'm'; % set color for limit line end; % draw axis with solid black color hh = line([x1,x2],[0,0]); set(hh,'LineWidth',1,'Color','k'); hv = line([0,0],[x1,x2]); set(hv,'LineWidth',1,'Color','k'); % start drawing the lines h1 = line([x1 x2], [y1,y2]); if (typ == 'n')     set(h1,'LineWidth',2,'LineStyle','--','Color',str1); else    set(h1,'LineWidth',1,'LineStyle','-','Color',str1); end if (b ~= 0)&(a ~= 0)    text(x1,y1,num2str(c)); end if( b == 0)|(a == 0)| (typ == 'n') | (typ == 'e')    grid    ret = [h1];    return, end  grid; h2 = line([x1 x2], [y1n,y2n]); set(h2,'LineWidth',0.5,'LineStyle',':','Color',str2); grid hold on ret = [h1 h2];

% Ex3_3.m

% Example 3.3 %  Optimization Using MATLAB by P.Venkataraman % % Using drawLine.m  % drawLine(0,6,1,1,5,'l');

第一条线

画了过后

第一根线是绿线, 第二根线是红线, 表示绿线的左下部分是可行区域

drawLine(0,6,2,1,4,'e');

第二条线

画了过后, 这里用紫线表示

drawLine(0,6,1,1,1,'g');

第三条线

画了过后

红线在此绿线的左下角,则说明可行区域在绿线的右上角部分

drawLine(0,6,2,-1,8,'n');

目标函数

画完过后,这里用蓝虚线表示,这里目标函数的意义为与Y轴截距的负值

xlabel('Hours spent studying'); ylabel('Hours of pin ball'); title('Example 3.3 -Equality Constraint and Negative Design Variables') grid