# 线性规划简介

## 线性规划问题的描述¶

$x_1$ 为花费在修路广告上的钱（千美元）

$x_2$ 为花费在枪支管制广告上的钱（千美元）

$x_3$ 为花费在农场补贴广告上的钱（千美元）

$x_4$ 为花费在汽油税广告上的钱（千美元）

$-2x_1+8x_2+0x_3+10x_4 \geq 50$

$5x_1+2x_2+0x_3+0x_4 \geq 100$

$3x_1-5x_2+10x_3-2x_4 \geq 25$

$x_1,x_2,x_3,x_4 \geq 0$

$-2x_1+8x_2+0x_3+10x_4\geq50$

$5x_1+2x_2+0x_3+0x_4\geq100$

$3x_1-5x_2+10x_3-2x_4\geq25$

$x_1,x_2,x_3,x_4\geq0$

## 图解法¶

$x+2y\leq8$

$x\leq4$

$y\geq3$

$x,y\in N$

$x\leq4$（红色区域） $y\geq3$（黑色区域） $x+2y\leq8$（深红色区域以及包含于 $\geq4$ 区域的浅红色区域）
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