Question

17．已知x，y滿足$\left\{\begin{array}{l}|{x-y}|≤2\\|{x+y}|≤1\end{array}\right.$，則z=2x-y的最大值為（　�。�

• A． $\frac{3}{2}$
• B． $\frac{5}{2}$
• C． $\frac{7}{2}$
• D． $\frac{9}{2}$

Answer 1

分析 作出可行域，平移目標(biāo)直線可得取最值時(shí)的條件，求交點(diǎn)代入目標(biāo)函數(shù)即可．

解答 解：由$\left\{\begin{array}{l}|{x-y}|≤2\\|{x+y}|≤1\end{array}\right.$，則$\left\{\begin{array}{l}{-2≤x-y≤2}\\{-1≤x+y≤1}\end{array}\right.$，滿足條件的可行域?yàn)椋?br />當(dāng)目標(biāo)直線過(guò)直線x-y=2與直線x+y=1的交點(diǎn)A（$\frac{3}{2}$，-$\frac{1}{2}$）時(shí)取最大值，
故最大值為z=2×$\frac{3}{2}$-（-$\frac{1}{2}$）=$\frac{7}{2}$
故答案為：$\frac{7}{2}$

點(diǎn)評(píng) 本題考查簡(jiǎn)單線性規(guī)劃，準(zhǔn)確作圖是解決問(wèn)題的關(guān)鍵，屬中檔題．