2020屆高考數(shù)學(xué)一輪復(fù)習(xí)6.2簡(jiǎn)單的線性規(guī)劃問題課件

1、2020屆高考數(shù)學(xué)一輪復(fù)習(xí)62020屆高考數(shù)學(xué)一輪復(fù)習(xí)620102019年高考全國(guó)卷考情一覽表 20102019年高考全國(guó)卷考情一覽表 2020屆高考數(shù)學(xué)一輪復(fù)習(xí)62020屆高考數(shù)學(xué)一輪復(fù)習(xí)62020屆高考數(shù)學(xué)一輪復(fù)習(xí)6考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74考點(diǎn)70平面區(qū)域問題 A.-3B.1C. D.3 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74考點(diǎn)70平面區(qū)域問題考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74解析如圖,要使不等式組表示的平面區(qū)域?yàn)槿切?則不等式x-y+2m0表示的平面區(qū)域?yàn)橹本€x-y+2m=0下方的區(qū)域,且-2m-1.這時(shí)平面區(qū)域?yàn)槿切蜛BC.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73

2、考點(diǎn)74解析如圖,要使不等式考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)742.(2014安徽,文13,5分,難度)不等式組 表示的平面區(qū)域的面積為4.解析畫出可行域,如圖陰影區(qū)域ABC(包括邊界),易得B(2,0),C(0,2),D(4,0),考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)742.(2014安徽考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74考點(diǎn)71簡(jiǎn)單的線性規(guī)劃問題1.(2019天津,理2文2,5分,難度)設(shè)變量x,y滿足約束條件A.2B.3C.5D.6命題點(diǎn)線性規(guī)劃.解題思路畫出可行域,平移目標(biāo)函數(shù),確定最大值.解析畫出可行域如圖,平移目標(biāo)函數(shù)z=-4x+y可知過點(diǎn)A時(shí)取得最大值,則目標(biāo)函數(shù)z=-

3、4x+y的最大值為 (C) 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74考點(diǎn)71簡(jiǎn)單的線性規(guī)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)742.(2019浙江,3,4分,難度)若實(shí)數(shù)x,y滿足約束條件則z=3x+2y的最大值是(C)A.-1B.1C.10D.12解析在平面直角坐標(biāo)系內(nèi)畫出題中的不等式組表示的平面區(qū)域?yàn)橐?-1,1),(1,-1),(2,2)為頂點(diǎn)的三角形區(qū)域(包含邊界),由圖易得當(dāng)直線z=3x+2y經(jīng)過平面區(qū)域內(nèi)的點(diǎn)(2,2)時(shí),z=3x+2y取得最大值z(mì)max=32+22=10.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)742.(2019浙江考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)743.(201

4、8天津,理2文2,5分,難度)設(shè)變量x,y滿足約束條件則目標(biāo)函數(shù)z=3x+5y的最大值為 (C) A.6B.19 C.21D.45 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)743.(2018天津考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)744.(2017全國(guó)2,理5文7,5分,難度)設(shè)x,y滿足約束條件則z=2x+y的最小值是(A) A.-15 B.-9 C.1 D.9解析畫出不等式組所表示的平面區(qū)域如圖所示,結(jié)合目標(biāo)函數(shù)z=2x+y的幾何意義,可得z在點(diǎn)B(-6,-3)處取得最小值,即zmin=-12-3=-15,故選A.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)744.(2017全國(guó)考點(diǎn)70考點(diǎn)71考點(diǎn)7

5、2考點(diǎn)73考點(diǎn)745.(2017全國(guó)3,文5,5分,難度)設(shè)x,y滿足約束條件 則z=x-y的取值范圍是(B) A.-3,0B.-3,2C.0,2D.0,3解析畫出不等式組表示的可行域,如圖.結(jié)合目標(biāo)函數(shù)的幾何意義,可得目標(biāo)函數(shù)在點(diǎn)A(0,3)處取得最小值z(mì)=0-3=-3,在點(diǎn)B(2,0)處取得最大值z(mì)=2-0=2.故選B.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)745.(2017全國(guó)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74 求簡(jiǎn)單的線性規(guī)劃問題的最值,要分析截距與z的關(guān)系,如z=2x+y,即y=-2x+z,截距與z相同,故截距越大,z越大,反之亦然;再如z=x-y,即y=x-z,截距與z互為相反

6、數(shù),故截距越大,z越小.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)746.(2017全國(guó)1,文7,5分,難度)設(shè)x,y滿足約束條件 則z=x+y的最大值為(D)A.0B.1C.2D.3解析根據(jù)題意作出可行域,如圖陰影部分所示.由z=x+y得y=-x+z.作出直線y=-x,并平移該直線,當(dāng)直線y=-x+z過點(diǎn)A時(shí),目標(biāo)函數(shù)取得最大值.由圖知A(3,0),故zmax=3+0=3.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)746.(2017全國(guó)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)747.(2016北京,理2,5分,難度)若x,y滿足 則2x+y的最大值為(C)A.0B.

7、3C.4D.5解析由不等式組可作出如圖的可行域(陰影部分),將z=2x+y變形為y=-2x+z,這是斜率為-2,隨z變化的一族平行直線,如圖,可知當(dāng)y=-2x+z經(jīng)過點(diǎn)P時(shí),z取最大值.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)747.(2016北京考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)748.(2016天津,理2,5分,難度)設(shè)變量x,y滿足約束條件A.-4B.6 C.10D.17解析如圖,作出變量x,y滿足約束條件表示的可行域,為三角形ABC及其內(nèi)部,點(diǎn)A,B,C的坐標(biāo)依次為(0,2),(3,0),(1,3).由圖可知,將考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)748.(2016天津考點(diǎn)70考點(diǎn)71考

8、點(diǎn)72考點(diǎn)73考點(diǎn)749.(2014全國(guó)2,理9,5分,難度)設(shè)x,y滿足約束條件則z=2x-y的最大值為(B)A.10 B.8C.3 D.2解析線性目標(biāo)函數(shù)z=2x-y滿足的可行域如圖所示.將直線l0:y=2x平行移動(dòng),當(dāng)直線l0經(jīng)過點(diǎn)M(5,2)時(shí),直線y=2x-z在y軸上的截距最小,也就是z取最大值,此時(shí)zmax=25-2=8.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)749.(2014全國(guó)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7410.(2014全國(guó)2,文9,5分,難度)設(shè)x,y滿足約束條件A.8B.7C.2D.1解析畫出可行域如圖所示,平移直線l0,當(dāng)直線過點(diǎn)A(3,2)時(shí),使得z最大,此時(shí)

9、,zmax=3+22=7.故選B.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7410.(2014全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7411.(2013全國(guó)2,文3,5分,難度)設(shè)x,y滿足約束條件則z=2x-3y的最小值是(B)A.-7B.-6 C.-5D.-3解析作出可行域如圖陰影部分所示.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7411.(2013全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7412.(2012全國(guó),文5,5分,難度)已知正三角形ABC的頂點(diǎn)A(1,1),B(1,3),頂點(diǎn)C在第一象限,若點(diǎn)(x,y)在ABC內(nèi)部,則z=-x+y的取值范圍是(A)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74

10、12.(2012全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7413.(2010全國(guó),文11,5分,難度)已知ABCD的三個(gè)頂點(diǎn)為A(-1,2),B(3,4),C(4,-2),點(diǎn)(x,y)在ABCD的內(nèi)部,則z=2x-5y的取值范圍是(B)A.(-14,16)B.(-14,20)C.(-12,18)D.(-12,20)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7413.(2010全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7414.(2019全國(guó)2,文13,5分,難度)若變量x,y滿足約束條件解析畫出可行域?yàn)閳D中陰影部分,z=3x-y表示直線3x-y-z=0的縱截距的相反數(shù),當(dāng)直線3x-y-z=0過點(diǎn)C(3,0

11、)時(shí),z取得最大值9.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7414.(2019全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7415.(2018全國(guó)1,理13文14,5分,難度)若x,y滿足約束條件解析作出可行域,如圖陰影部分所示(包括邊界). 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7415.(2018全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7416.(2018全國(guó)2,理14文14,5分,難度)若x,y滿足約束條件解析由題意,作出可行域如圖.要使z=x+y取得最大值,當(dāng)且僅當(dāng)過點(diǎn)(5,4)時(shí),zmax=9.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7416.(2018全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)741

12、7.(2018全國(guó)3,文15,5分,難度)若變量x,y滿足約束條件 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7417.(2018全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7418.(2018北京,理12文13,5分,難度)若x,y滿足x+1y2x,則2y-x的最小值是3.作出不等式組對(duì)應(yīng)的可行域,如下圖陰影部分所示. 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7418.(2018北考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7419.(2018浙江,12,6分,難度)若x,y滿足約束條件則z=x+3y的最小值是-2,最大值是8.解析畫出可行域,如圖陰影部分所示.由題意可知,當(dāng)目標(biāo)函數(shù)的圖象經(jīng)過點(diǎn)B時(shí),z取得最大值,

13、當(dāng)目標(biāo)函數(shù)的圖象經(jīng)過點(diǎn)C時(shí),z取得最小值.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7419.(2018浙考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7420.(2017全國(guó)3,理13,5分,難度)若x,y滿足約束條件考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7420.(2017全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7421.(2017全國(guó)1,理14,5分,難度)設(shè)x,y滿足約束條件 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7421.(2017全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7422.(2016全國(guó)3,理13,5分,難度)若x,y滿足約束條件 解析作出不等式組滿足的平面區(qū)域如圖陰影部分所示. 考點(diǎn)70考點(diǎn)71考

14、點(diǎn)72考點(diǎn)73考點(diǎn)7422.(2016全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7423.(2016全國(guó)2,文14,5分,難度)若x,y滿足約束條件 解析作出可行域,如圖陰影部分所示. 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7423.(2016全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7424.(2016全國(guó)3,文13,5分,難度)設(shè)x,y滿足約束條件 解析滿足已知條件的可行域?yàn)槿鐖D所示的陰影部分,其中A(1,0),B(-1,-1),C(1,3). 當(dāng)直線經(jīng)過點(diǎn)B時(shí),直線在y軸上的截距最小,即z最小.故zmin=2(-1)+3(-1)-5=-10. 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7424.(201

15、6全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7425.(2015全國(guó)2,理14,5分,難度)若x,y滿足約束條件 解析由約束條件畫出可行域,如圖中的陰影部分所示. 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7425.(2015全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7426.(2015全國(guó)2,文14,5分,難度)若x,y滿足約束條件 解析如圖所示,可行域?yàn)殛幱安糠? 由可行域可知,目標(biāo)函數(shù)z=2x+y過點(diǎn)B取得最大值.則B(3,2),故zmax=6+2=8. 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7426.(2015全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7427.(2015全國(guó)1,文15,5分,難度)若x,

16、y滿足約束條件 解析畫出約束條件對(duì)應(yīng)的可行域(如圖陰影部分所示),由 即點(diǎn)A的坐標(biāo)為(1,1).由z=3x+y,得y=-3x+z.作出直線l0:y=-3x,并平移,當(dāng)直線經(jīng)過點(diǎn)A時(shí),直線在y軸上的截距最大,即z最大.所以zmax=31+1=4.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7427.(2015全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7428.(2013全國(guó)1,文14,5分,難度)設(shè)x,y滿足約束條件 解析畫出可行域如圖所示.畫出直線2x-y=0,并平移,當(dāng)直線經(jīng)過點(diǎn)A(3,3)時(shí),z取最大值,且最大值為z=23-3=3.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7428.(2013全考點(diǎn)70考點(diǎn)

17、71考點(diǎn)72考點(diǎn)73考點(diǎn)7429.(2012全國(guó),理14,5分,難度)設(shè)x,y滿足約束條件解析作出不等式組的可行域,如圖陰影部分,作直線l0:x-2y=0,在可行域內(nèi)平移知過點(diǎn)A時(shí),z=x-2y取得最大值,過點(diǎn)B時(shí),z=x-2y取得最小值.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7429.(2012全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7430.(2011全國(guó),文14,5分,難度)若變量x,y滿足約束條件 解析由約束條件作出可行域如圖所示,知z=x+2y在點(diǎn)A處取得最小值. 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)7430.(2011全考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74考點(diǎn)72非線性目標(biāo)函數(shù)問題

18、1.(2016山東,理4文4,5分,難度)若變量x,y滿足則x2+y2的最大值是(C)A.4B.9 C.10 D.12解析如圖,不等式組表示的可行域是以A(0,-3),B(0,2),C(3,-1)為頂點(diǎn)的三角形區(qū)域,x2+y2表示點(diǎn)(x,y)到原點(diǎn)距離的平方,最大值必在頂點(diǎn)處取到,經(jīng)驗(yàn)證最大值|OC|2=10,故選C.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74考點(diǎn)72非線性目標(biāo)函考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)742.(2016浙江,理3,5分,難度)在平面上,過點(diǎn)P作直線l的垂線所在直線x+y-2=0上的投影構(gòu)成的線段記為AB,則|AB|=(C)解析作出不等式組所表示的平面區(qū)域,如圖中陰影

19、部分所示,過點(diǎn)C,D分別作直線x+y-2=0的垂線,垂足分別為A,B,則四邊形ABDC為矩形.又D(2,-2),C(-1,1),所以考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)742.(2016浙江考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74斜率為1的平行直線之間,則這兩條平行直線間的距離的最小值是(B)解析作出可行域,如圖陰影部分所示.兩平行直線的斜率為1,兩平行直線與直線x+y-3=0垂直.兩平行線間的最短距離是AB的長(zhǎng)度.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74斜率為1的平行直線之考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)744.(2015全國(guó)1,理15,5分,難度)若x,y滿足約束條件的最大值為3. 考

20、點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)744.(2015全國(guó)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74 非線性目標(biāo)函數(shù)的線性規(guī)劃問題關(guān)鍵在于目標(biāo)函數(shù)的轉(zhuǎn)化,可通過整理變形,或幾何意義轉(zhuǎn)化為常見問題求解.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74考點(diǎn)73求參數(shù)問題 若z=ax+y的最大值為4,則a=(B)A.3B.2C.-2D.-3考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74考點(diǎn)73求參數(shù)問題考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74解析由約束條件畫出可行域,如圖陰影部分所示.線性目標(biāo)函數(shù)z=ax+y,即y=-ax+z.設(shè)直線l0:ax+y=0.當(dāng)-a1,即a-1時(shí),

21、l0過O(0,0)時(shí),z取得最大值,zmax=0+0=0,不合題意;當(dāng)0-a1,即-1a0時(shí),l0過B(1,1)時(shí),z取得最大值,zmax=a+1=4,a=3(舍去);當(dāng)-1-a0時(shí),即0a1時(shí),l0過B(1,1)時(shí),z取得最大值,zmax=2a+1=4,a= (舍去);當(dāng)-a-1,即a1時(shí),l0過A(2,0)時(shí),z取得最大值,zmax=2a+0=4,a=2.綜上,a=2符合題意.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74解析由約束條件畫出可考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)742.(2015福建,文10,5分,難度)變量x,y滿足約束條件 A.-2B.-1 C.1 D.2解析作出可行域,如圖

22、所示.作直線2x-y=2,與直線x-2y+2=0交于可行域內(nèi)一點(diǎn)A(2,2),由題知直線mx-y=0必過點(diǎn)A(2,2),即2m-2=0,得m=1.故選C.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)742.(2015福建考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74且z=x+ay的最小值為7,則a=(B)A.-5B.3C.-5或3D.5或-3解析當(dāng)a=0時(shí)顯然不滿足題意.當(dāng)a1時(shí),畫出可行域(如圖(1)所示的陰影部分),圖(1) 圖(2)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74且z=x+ay的最小考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74當(dāng)a0時(shí),畫出可行域(如圖(3)所示的陰影部分), 圖(3) 考點(diǎn)70考

23、點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74當(dāng)a0,x,y滿足約束條件 考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)745.(2013全國(guó)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74考點(diǎn)74線性規(guī)劃的實(shí)際應(yīng)用1.(2018北京,理8文8,5分,難度)設(shè)集合A=(x,y)|x-y1,ax+y4,x-ay2,則(D)A.對(duì)任意實(shí)數(shù)a,(2,1)AB.對(duì)任意實(shí)數(shù)a,(2,1)AC.當(dāng)且僅當(dāng)a0時(shí),(2,1)AD.當(dāng)且僅當(dāng)a 時(shí),(2,1)A考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74考點(diǎn)74線性規(guī)劃的實(shí)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)742.(2015陜西,理10文11,5分,難度)某企業(yè)生產(chǎn)甲、乙兩種產(chǎn)品均需用A,B兩種原

24、料,已知生產(chǎn)1噸每種產(chǎn)品所需原料及每天原料的可用限額如表所示.如果生產(chǎn)1噸甲、乙產(chǎn)品可獲利潤(rùn)分別為3萬元、4萬元,則該企業(yè)每天可獲得最大利潤(rùn)為(D)A.12萬元B.16萬元C.17萬元D.18萬元考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)742.(2015陜西考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74解析設(shè)該企業(yè)每天生產(chǎn)甲產(chǎn)品x噸,乙產(chǎn)品y噸,獲利z元.則由題意畫出可行域如圖所示,當(dāng)直線3x+4y-z=0過點(diǎn)B時(shí),目標(biāo)函數(shù)取得最大值.考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74解析設(shè)該企業(yè)每天生產(chǎn)考點(diǎn)70考點(diǎn)71考點(diǎn)72考點(diǎn)73考點(diǎn)74有下面四個(gè)命題:p1:(x,y)D,x+2y-2,p2:(x,y)D,x+2y2,p3:(x,y)D,x+2y3,p4:(x,y)D,x+2y-1,其中的真命題是(B)A.p2,p3B.p1