A
分析:本題考查的知識(shí)點(diǎn)是簡(jiǎn)單的線性規(guī)劃,我們可以先畫出足約束條件的平面區(qū)域,再根據(jù)目標(biāo)函數(shù)z=ax+by(a>0,b>0)的值是最大值為6,得2a+3b=12,結(jié)合基本不等式中“1的活用”的方法,即可求出
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+
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的最小值.
解答:不等式組所表示的平面區(qū)域如圖中陰影部分所示,當(dāng)直線z=ax+by(a>0,b>0)過(guò)直線x-y+
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=0與直線6x-2y-3=0的交點(diǎn)(1,
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)時(shí),目標(biāo)函數(shù)z=ax+by(a>0,b>0)取得最大值6,即a+
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b=6,即2a+3b=12,而
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+
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=(
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+
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)(
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)=
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[13+6(
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+
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)]≥
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,當(dāng)且僅當(dāng)a=b時(shí)取等號(hào).
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故選A.
點(diǎn)評(píng):用圖解法解決線性規(guī)劃問(wèn)題時(shí),分析題目的已知條件,找出約束條件和目標(biāo)函數(shù)是關(guān)鍵,可先將題目中的量分類、列出表格,理清頭緒,然后列出不等式組(方程組)尋求約束條件,并就題目所述找出目標(biāo)函數(shù).然后將可行域各角點(diǎn)的值一一代入,最后比較,即可得到目標(biāo)函數(shù)的最優(yōu)解.