Question

6．若x，y滿足$\left\{\begin{array}{l}x+y≥0\\ x≥1\\ x-y≥0\end{array}\right.$，則下列不等式恒成立的是（　�。�

• A． y≥-1
• B． x≥2
• C． x+2y+2≥0
• D． 2x-y+1≥0

Answer 1

分析 由約束條件作出可行域，作出四個(gè)選項(xiàng)中不等式所對(duì)應(yīng)的直線，由圖可得答案．

解答 解：由約束條件$\left\{\begin{array}{l}x+y≥0\\ x≥1\\ x-y≥0\end{array}\right.$作出可行域如圖，

由圖可知，對(duì)可行域內(nèi)的點(diǎn)不等式恒成立的是2x-y+1=0．
故選：D．

點(diǎn)評(píng) 本題考查了簡(jiǎn)單的線性規(guī)劃，考查了數(shù)形結(jié)合的解題思想方法，是中檔題．