标签：
剧情提要：正剧开始：
星历2016年04月17日 10:30:26, 银河系厄尔斯星球中华帝国江南行省。
[工程师阿伟]正在和[机器小伟]一起研究[不等式]。
图中绿色部分取值表示A公司划算，否则就是B公司划算了。
<span style="font-size:18px;"> if (1) {
var r = 20;
config.setSector(1,1,1,1);
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,190);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 2, spaceY = 2;
var xS = -10, xE = 10;
var yS = -10, yE = 10;
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
//
var arrayYes = [], arrayNo= [];
//系数阵列 ax^2+bx+c
var coeffecient = [1, -5, 0];
var yVal = 0;
for (var x = xS; x <= xE; x+=0.3) {
yVal = 0;
for (var i = 0; i < coeffecient.length; i++) {
yVal *= x;
yVal += coeffecient[i];
}
if (yVal <= 0) {
arrayYes.push([x, yVal]);
}
else {
arrayNo.push([x, yVal]);
}
}
var transform = new Transform();
var tmp = [];
if (arrayNo.length > 0) {
arrayNo = transform.scale(transform.translate(arrayNo, 0, 0), scaleX/spaceX, scaleY/spaceY);
//不满足条件的点
tmp = [].concat(arrayNo);
shape.pointDraw(tmp, 'blue');
tmp = [].concat(arrayNo);
shape.strokeDraw(tmp, 'blue');
}
if (arrayYes.length > 0) {
arrayYes = transform.scale(transform.translate(arrayYes, 0, 0), scaleX/spaceX, scaleY/spaceY);
//满足条件的点 --> 解集
tmp = [].concat(arrayYes);
shape.pointDraw(tmp, 'green');
tmp = [].concat(arrayYes);
shape.strokeDraw(tmp, 'green');
}
}
</span>
<span style="font-size:18px;"> if (1) {
var mathText = new MathText();
var s = [
'(-b± |Δ^[0.5])/2a',
'-b/2a',
'[-[INF], (-b- |Δ^[0.5])/2a), ((-b+ |Δ^[0.5])/2a, [INF]]',
'R',
'( (-b- |Δ^[0.5])/2a, (-b+ |Δ^[0.5])/2a )',
];
var x =40, y=40;
var r1 = 40;
var len = s.length;
for (var i = 0; i < len; i++) {
if (s[i] == '') {
if (x < 100) {
x += 300;
y-=r1*3;
}
else {
x = 20;
y += r1;
}
}
else {
mathText.printSet(s[i], x, y, 'red');
y+=r1;
}
}
}</span>
<span style="font-size:18px;">function Equation() {
this.quadratic = function(array) {
//array = [a, b, c]
//满足ax2 + bx + c = 0 (a!=0)
var a = array[0], b = array[1], c = array[2];
if (a < 0) {
a = -a;
b = -b;
c = -c;
}
var p = 0, q = 0, delta = 0;
var x1 = 0, x2 = 0;
var s = '';
if (a == 0) {
s = '方程 '+b.toString()+'x + '+c.toString()+' = 0 =>';
document.write(s+'<br/>');
x1 = -c / b;
s = '方程的解为：x = '+x1.toString()+' ;';
}
else {
s = '方程 '+a.toString()+'x^[2] + '+b.toString()+'x + '+c.toString()+' = 0 =>';
document.write(s+'<br/>');
delta = b*b-4*a*c;
s = 'Δ = b^[2] - 4ac = ' + delta.toString()+' ;';
document.write(s+'<br/>');
if (delta < 0) {
s = '没有实数解。';
document.write(s+'<br/>');
}
else {
if (Math.abs(delta) < 0.000001) {
x1 = x2 = -b/(2*a);
s = '方程的解为：x1 = x2 = '+x1.toString()+' ;';
}
else if (delta > 0) {
x1 = (-b-Math.sqrt(delta))/(2*a);
x2 = (-b+Math.sqrt(delta))/(2*a);
s = '方程的解为：x1 = '+x1.toString()+', x2 = '+x2.toString()+' ;';
}
document.write(s+'<br/>');
p = x1+x2;
q = x1*x2;
s = '方程根与系数的关系：x1 + x2 = ' + p.toString()+', x1 * x2 = '+q.toString()+' ;';
document.write(s+'<br/>');
document.write(''+'<br/>');
}
}
}
}
if (1) {
var equation = new Equation();
equation.quadratic([4, -4, 1]);
}
方程 4x^[2] + -4x + 1 = 0 =>
Δ = b^[2] - 4ac = 0 ;
方程的解为：x1 = x2 = 0.5 ;
方程根与系数的关系：x1 + x2 = 1, x1 * x2 = 0.25 ;
if (1) {
var equation = new Equation();
equation.quadratic([-1, 2, -3]);
}
方程 1x^[2] + -2x + 3 = 0 =>
Δ = b^[2] - 4ac = -8 ;
没有实数解。
</span>
<span style="font-size:18px;"> if (1) {
var r = 20;
config.setSector(1,1,1,1);
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,190);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 2, spaceY = 2;
var xS = -10, xE = 10;
var yS = -10, yE = 10;
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
//
var arrayYes = [], arrayNo= [];
//系数阵列 ax^2+bx+c
var coeffecient = [4, -4, 1];
var yVal = 0;
for (var x = xS; x <= xE; x+=0.3) {
yVal = 0;
for (var i = 0; i < coeffecient.length; i++) {
yVal *= x;
yVal += coeffecient[i];
}
if (yVal > 0) {
arrayYes.push([x, yVal]);
}
else {
arrayNo.push([x, yVal]);
}
}
var transform = new Transform();
var tmp = [];
if (arrayNo.length > 0) {
arrayNo = transform.scale(transform.translate(arrayNo, 0, 0), scaleX/spaceX, scaleY/spaceY);
//不满足条件的点
tmp = [].concat(arrayNo);
shape.pointDraw(tmp, 'blue');
tmp = [].concat(arrayNo);
shape.strokeDraw(tmp, 'blue');
}
if (arrayYes.length > 0) {
arrayYes = transform.scale(transform.translate(arrayYes, 0, 0), scaleX/spaceX, scaleY/spaceY);
//满足条件的点 --> 解集
tmp = [].concat(arrayYes);
shape.pointDraw(tmp, 'green');
tmp = [].concat(arrayYes);
shape.strokeDraw(tmp, 'green');
}
}
</span>
蓝色表示非解集，所以这个无解。
<span style="font-size:18px;"> if (1) {
var r = 20;
config.setSector(1,1,1,1);
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,190);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 2, spaceY = 2;
var xS = -10, xE = 10;
var yS = -10, yE = 10;
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
//
var arrayYes = [], arrayNo= [];
//系数阵列 ax^2+bx+c
var coeffecient = [-1, 2, -3];
var yVal = 0;
for (var x = xS; x <= xE; x+=0.3) {
yVal = 0;
for (var i = 0; i < coeffecient.length; i++) {
yVal *= x;
yVal += coeffecient[i];
}
if (yVal > 0) {
arrayYes.push([x, yVal]);
}
else {
arrayNo.push([x, yVal]);
}
}
var transform = new Transform();
var tmp = [];
if (arrayNo.length > 0) {
arrayNo = transform.scale(transform.translate(arrayNo, 0, 0), scaleX/spaceX, scaleY/spaceY);
//不满足条件的点
tmp = [].concat(arrayNo);
shape.pointDraw(tmp, 'blue');
tmp = [].concat(arrayNo);
shape.strokeDraw(tmp, 'blue');
}
if (arrayYes.length > 0) {
arrayYes = transform.scale(transform.translate(arrayYes, 0, 0), scaleX/spaceX, scaleY/spaceY);
//满足条件的点 --> 解集
tmp = [].concat(arrayYes);
shape.pointDraw(tmp, 'green');
tmp = [].concat(arrayYes);
shape.strokeDraw(tmp, 'green');
}
}</span>
<span style="font-size:18px;"> if (1) {
var r = 20;
config.setSector(1,1,1,1);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 2, spaceY = 2;
var xS = -10, xE = 10;
var yS = -10, yE = 10;
//
var arrayYes = [], arrayNo= [];
//系数阵列 ax + by + c
var coeffecient = [1, 4, -4];
var yes = 0, no = 0;
for (var x = xS; x <= xE; x+=0.5) {
for (var y = yS; y <= yE; y+=0.5) {
//条件
yes = (coeffecient[0]*x+coeffecient[1]*y+coeffecient[2] < 4);
if (yes) {
arrayYes.push([x, y]);
}
else {
arrayNo.push([x, y]);
}
}
}
var transform = new Transform();
var tmp = [];
if (arrayNo.length > 0) {
arrayNo = transform.scale(transform.translate(arrayNo, 0, 0), scaleX/spaceX, scaleY/spaceY);
//不满足条件的点
tmp = [].concat(arrayNo);
shape.pointDraw(tmp, '#CC88FF');
/*tmp = [].concat(arrayNo);
shape.strokeDraw(tmp, 'blue'); */
}
if (arrayYes.length > 0) {
arrayYes = transform.scale(transform.translate(arrayYes, 0, 0), scaleX/spaceX, scaleY/spaceY);
//满足条件的点 --> 解集
tmp = [].concat(arrayYes);
shape.pointDraw(tmp, '#CCFF88');
/*tmp = [].concat(arrayYes);
shape.strokeDraw(tmp, 'green'); */
}
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,190);
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
}
</span>
<span style="font-size:18px;"> if (1) {
var r = 20;
config.setSector(1,1,1,1);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 3, spaceY = 5;
var xS = -10, xE = 20;
var yS = -10, yE = 20;
//
var arrayYes = [], arrayNo= [];
//系数阵列 ax + by + c
var coeffecient = [];
var yes = 0, no = 0;
for (var x = xS; x <= xE; x+=0.5) {
for (var y = yS; y <= yE; y+=0.5) {
//条件
yes = (2*x + y >= 15) &&
(x+2*y>=18) &&
(x+3*y>=27) &&
(x >= 0) &&
(y >= 0);
if (yes) {
arrayYes.push([x, y]);
}
else {
arrayNo.push([x, y]);
}
}
}
var transform = new Transform();
var tmp = [];
if (arrayNo.length > 0) {
arrayNo = transform.scale(transform.translate(arrayNo, 0, 0), scaleX/spaceX, scaleY/spaceY);
//不满足条件的点
tmp = [].concat(arrayNo);
shape.pointDraw(tmp, '#CC88FF');
/*tmp = [].concat(arrayNo);
shape.strokeDraw(tmp, 'blue'); */
}
if (arrayYes.length > 0) {
arrayYes = transform.scale(transform.translate(arrayYes, 0, 0), scaleX/spaceX, scaleY/spaceY);
//满足条件的点 --> 解集
tmp = [].concat(arrayYes);
shape.pointDraw(tmp, '#CCFF88');
/*tmp = [].concat(arrayYes);
shape.strokeDraw(tmp, 'green'); */
}
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,190);
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
}
</span>
<span style="font-size:18px;"> if (1) {
var r = 20;
config.setSector(1,1,1,1);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 1, spaceY = 1;
var xS = 0, xE = 5;
var yS = 0, yE = 5;
//
var arrayYes = [], arrayNo= [];
//系数阵列 ax + by + c
var coeffecient = [];
var yes = 0, no = 0;
for (var x = xS; x <= xE; x+=1) {
for (var y = yS; y <= yE; y+=1) {
//条件
yes = (x+2*y<=8) &&
(4*x<=16) &&
(4*y<=12) &&
(x >= 0) &&
(y >= 0);
if (yes) {
arrayYes.push([x, y]);
}
else {
arrayNo.push([x, y]);
}
}
}
//可行域与最优解
var size = arrayYes.length;
var feasible = [];
for (var i = 0; i < size; i++) {
feasible.push([arrayYes[i][0], arrayYes[i][1], arrayYes[i][0]*2+arrayYes[i][1]*3]);
}
feasible.sort(function(a, b) {
//求最小值为最优时不加负号
//最大值为最优时加负号
return -(a[2]-b[2]);
});
var best = [feasible[0][0]*scaleX/spaceX, feasible[0][1]*scaleY/spaceY];
var s = '最优解是：'+feasible[0][0].toFixed(3)+' , ' + feasible[0][1].toFixed(3)+' , ' +feasible[0][2].toFixed(3);
plot.fillText(s, -270, -170, 200);
//区域图
var transform = new Transform();
var tmp = [];
if (arrayNo.length > 0) {
arrayNo = transform.scale(transform.translate(arrayNo, 0, 0), scaleX/spaceX, scaleY/spaceY);
//不满足条件的点
tmp = [].concat(arrayNo);
shape.pointDraw(tmp, '#CC88FF');
/*tmp = [].concat(arrayNo);
shape.strokeDraw(tmp, 'blue'); */
}
if (arrayYes.length > 0) {
arrayYes = transform.scale(transform.translate(arrayYes, 0, 0), scaleX/spaceX, scaleY/spaceY);
//满足条件的点 --> 解集
tmp = [].concat(arrayYes);
shape.pointDraw(tmp, '#CCFF88');
/*tmp = [].concat(arrayYes);
shape.strokeDraw(tmp, 'green'); */
}
//最优点绘制
shape.pointDraw(best, 'red');
//坐标轴标注
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,190);
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
}</span>
这个Excel解决的是这个问题：
<span style="font-size:18px;"> if (1) {
var r = 20;
config.setSector(10,5,9.5,1);
//坐标轴设定
var scaleX = 2*r, scaleY = 2*r;
var spaceX = 0.1, spaceY = 0.1;
var xS = 0, xE = 1;
var yS = 0, yE = 0.8;
//
var arrayYes = [], arrayNo= [];
//系数阵列 ax + by + c
var coeffecient = [];
var yes = 0, no = 0;
for (var x = xS; x <= xE; x+=0.01) {
for (var y = yS; y <= yE; y+=0.01) {
//条件
yes = (0.105*x+0.105*y>=0.075) &&
(0.07*x+0.14*y>=0.06) &&
(0.14*x+0.07*y>=0.06) &&
(x >= 0) &&
(y >= 0);
if (yes) {
arrayYes.push([x, y]);
}
else {
arrayNo.push([x, y]);
}
}
}
//可行域与最优解
var size = arrayYes.length;
var feasible = [];
for (var i = 0; i < size; i++) {
feasible.push([arrayYes[i][0], arrayYes[i][1], arrayYes[i][0]*28+arrayYes[i][1]*21]);
}
feasible.sort(function(a, b) {
return (a[2]-b[2]);
});
var best = [feasible[0][0]*scaleX/spaceX, feasible[0][1]*scaleY/spaceY];
//区域图
var transform = new Transform();
var tmp = [];
if (arrayNo.length > 0) {
arrayNo = transform.scale(transform.translate(arrayNo, 0, 0), scaleX/spaceX, scaleY/spaceY);
//不满足条件的点
tmp = [].concat(arrayNo);
shape.pointDraw(tmp, '#CC88FF');
/*tmp = [].concat(arrayNo);
shape.strokeDraw(tmp, 'blue'); */
}
if (arrayYes.length > 0) {
arrayYes = transform.scale(transform.translate(arrayYes, 0, 0), scaleX/spaceX, scaleY/spaceY);
//满足条件的点 --> 解集
tmp = [].concat(arrayYes);
shape.pointDraw(tmp, '#CCFF88');
/*tmp = [].concat(arrayYes);
shape.strokeDraw(tmp, 'green'); */
}
//最优点绘制
shape.pointDraw(best, 'red');
//坐标轴标注
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0,350);
config.axisSpacing(xS, xE, spaceX, scaleX, 'X');
config.axisSpacing(yS, yE, spaceY, scaleY, 'Y');
var s = '最优解是：'+feasible[0][0].toFixed(3)+' , ' + feasible[0][1].toFixed(3)+' , ' +feasible[0][2].toFixed(3);
plot.setFillStyle('blue')
.fillText(s, 270, -340, 200);
}</span>
本节到此结束，欲知后事如何，请看下回分解。
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原文地址：http://blog.csdn.net/mwsister/article/details/51172034
