问题 解答题
某企业某年生产某种产品,通过合理定价及促销活动,确保产销平衡(根据市场情况确定产量,使该年所生产产品刚好全部销售完毕),年产量、年销量均为x万件.已知每生产1万件产品需投入32万元的生产费用,另外该年生产设备折旧、维修等固定费用总共为4万元.每件产品定价为平均每件生产成本的150%进行销售,年销量x万件与年促销费用t万元之间满足关系:6-x=
k
t+1
(k为常数),当年促销费用t=0万元时年销量是x=2万件.
(Ⅰ)将年的利润y(万元)表示为促销费t(万元)的函数;
(Ⅱ)该企业年促销费投入多少万元时,企业年利润最大?相应年产量及最大年利润为多少?
注:生产成本=固定费用+生产费用  (不包括促销费用)
利润=销售收入-生产成本-促销费.
答案

(Ⅰ)依题意,x=6-

k
t+1
,将t=0,x=2代入得k=4,

∴年销售量x=6-

4
t+1
,t≥0.

依题意,产销平衡即年产量等于年销量x万件,

∴当年生产量为x万件时,

年生产成本=32x+4=32(6-

4
t+1
)+4=196-
128
t+1

平均每件产品生产成本=(196-

128
t+1
)÷x,

年销售收入=[(196-

128
t+1
)÷x]×
3
2
x
=
3
2
(196-
128
t+1
)

∴年利润y=

3
2
(196-
128
t+1
)-(196-
128
t+1
)-t=98-
64
t+1
-t,t≥0.

(Ⅱ)∵y=98-

64
t+1
-t=99-(t+1+
64
t-1
),t≥0

∴t+1+

64
t+1
≥2
(t+1)•
64
t+1
=16,

∴当且仅当t+1=

64
t+1
,即t=7时,ymax=99-16=83.

∴当促销费投入7万元时,企业年利润最大,

此时年产量x=5.5万件,年利润最大值为83万元.

阅读理解

     The sun was shining as Kevin walked to the old bench(长凳) where he met Mike every afternoon after school. They were good friends and loved to play football. They didn't have enough money to buy a real football, but Mike had made a ball out of old socks covered with a piece of plastic. It wasn't beautiful, but

it worked well. The two friends didn't stop kicking and running until very late.

     The next afternoon, Mike and Kevin met again at the old bench. Soon the home-made ball was

spinning(旋转) across the grass as the boys laughed and shouted happily. The ball was stopped by a

boy wearing a nice pair of sneakers(运动鞋). Kevin was upset when he saw it was Steven.

     The next morning, Kevin's mother gave him an envelope(信封). "Your uncle sent you a birthday

present," she smiled. Kevin's eyes grew big when he saw the $100 bill. Later that day, a pair of new

sneaker lay next to his chair, and in the corner, a real football.

     The next afternoon, Steven invited Kevin to play football on the field next to the library. Steven did

not want Mike to join them only because Mike's sneakers were dirty and he was not good at football.

When the game was over, Kevin and Steven walked past the old bench where Mike was sitting. Steven

picked up a stone and threw it at him. Kevin, holding his new football in his hands, walked on and did not

look back.

     One afternoon, as Kevin walked past the old bench, he saw something lying under it. He looked

closer and saw it was the home-made ball. Kevin was full of sorrow at the sight of his old home-made

ball, and he let out a sad sigh(叹气). As his sadness turned to anger, he picked up his new football and

kicked it into the air. Kevin kicked it so hard that it flew past the library and over the school gate. Then

Kevin walked to the bench and picked up his home-made ball. Holding it in his hands, Kevin sat down

and waited.

1. The best title for this passage is ______.

A. A Home-Made Football                

B. Playing Football

C. Two Close Friends                    

D. A New Football

填空题