问题 解答题
设z=2y-2x+4,式中x,y满足条件
0≤x≤1
0≤y≤2
2y-x≥1
,求z的最大值和最小值.
答案

作出不等式组对应的平面区域如图:

由z=2y-2x+4得y=x+

z
2
-2,

平移直线y=x+

z
2
-2,由图象可知当直线y=x+
z
2
-2
经过点A(0,2)时,

直线y=x+

z
2
-2的截距最大,此时z最大,zmax=2×2+4=8.

直线y=x+

z
2
-2经过点B时,直线y=x+
z
2
-2
的截距最小,此时z最小,

x=1
2y-x=1
,解得
x=1
y=1
,即B(1,1),此时zmin=2-2+4=4,

即z的最大值是8,最小值是4.

填空题

动词填空。阅读下面短文,用括号内所给动词的适当形式填空 (必要时可加情态动词或助动词)。

    My grandmother was an iron-willed (强硬的) woman. When I was five, she invited some friends to her

apartment. Among the guests there (1)_____ (be) a rich man and his daughter. Grandmother considered them

the most important among the guests.

    During the party, I went to the bathroom. I was still sitting down when the girl walked in. "You (2)____

(stay) here too long!"  

    It's not your business. Don't you know that little girls shouldn't come into the bathroom when a little boy

(3)_____ (use) it!?" I said in anger. This (4)______ (surprise) the little girl. Then she started to cry. Most guests

had heard what I said and laughed. But not Grandmother.

    She (5)______ (wait) for me when I left the bathroom. Grandmother shouted that I was impolite and rude

and ordered, "You (6)_____ (say) sorry to her." All the guests watched in silence.

    Twenty minutes later, Grandmother walked by the bathroom and noticed a torrent (激流) of water (7)____

(run) out from under the door. Everyone knew who did that. Grandmother was so angry that she tried (8)_____

(get) me anyway. It took several strong men finally to move her away and calm her down.

    My grandfather took me by the hand and seated me on his lap. He looked at me, not at all angry or upset.

"(9)_____ (tell) me," he asked, "why did you do it?" 

    "Well, she shouted at me for nothing," I said seriously. "Now she's got something to be angry at." 

    Grandfather didn't speak right away. He just sat there, looking at me and smiling. I (10)______ never _____

(forget) his expressions (表情) for my whole life. 

    "Eric," he said at last, "I think you did the right thing."

简答题