问题 解答题

工艺商场按标价销售某种工艺品时,每件可获利45元;按标价的八五折销售该工艺品8件与将标价降低35元销售该工艺品12件所获利润相等.

(1)该工艺品每件的进价、标价分别是多少元?

(2)若每件工艺品按(1)中求得的进价进货,标价售出,工艺商场每天可售出该工艺品100件.若每件工艺品降价1元,则每天可多售出该工艺品4件.问每件工艺品降价多少元出售,每天获得的利润最大?获得的最大利润是多少元?

(3)在(2)的情况下,物价部门规定该商场在该工艺品的经营上每天获得的利润不能超过4800元,而商场在该商品的经营中,每天所获得的利润不想低于4704元,应该如何定价该工艺品?

答案

(1)设该工艺品标价为x元/件,则进价为(x-45)元,

由题意可得:8[85%x-(x-45)]=12[x-35-(x-45)],

解这个方程得:x=200,

∴进价为:200-45=155,

答:这种工艺品的进价为155元,标价为200元.

(2)设每天所获得的利润为W元,每件降价m元,

则W=(45-m)(100+4m),

W=-4m2+80m+4500,

W=-4(m-10)2+4900,

当m=10时,W得到最大值为4900,

即当每件降价10元时,获利最多.为4900元.

(3)W=-4m2+80m+4500,

当w=4800时,

4800=-4m2+80m+4500,

解得:m=15或m=5,标价为195元或185元,

当w=4704时,

4704=-4m2+80m+4500,

解得m=17或m=3,标价为183元或197元,

由函数的图象可知,商品的售价不小于183元而不大于185元,或者售价不小于195元而不大于197元.

选择题
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Chinese mainland's star-making reality TV show "Happy Boy" will not be open to male applicants from Hong Kong, Taiwan, Macau or other foreign cities, said the country's top TV industry committee yesterday.

Happy Boy is the male version of Super Girl, which is regarded as the Chinese version of American Idol. The girl's event, operated by central China's Hunan TV, drew an audience of 400 million for the final match in 2005. The country's State Administration of Radio, Film and Television approved the male version earlier this month. However, the regulation that only mainland's male applicants are allowed to register was released just days before the application procedure began on Wednesday in Changsha, one of the five mainland cities to hold the contest. The other four includes Chengdu and three undecided cities.

The regulation spoiled Hunan TV's ambition to extend the series to the overseas market, an official with the TV station told the Hunan-based Xiaoxiang Morning yesterday. "My Hero," another star-making reality show by Shanghai's SMG Dragon TV, said it was not informed of the regulation, and it is still receiving foreign applicants, said an official with Dragon TV. A previous regulation by the administration has made clear that televised talent shows can't run for more than six weeks at a time. While the first "Happy Boy" may last for five months, according to a previous report.

Last year there were about 10 influential star-making TV shows across the country, among which those from CCTV, Hunan Satellite TV and SMG's Dragon TV, were the most popular. "Super Girl" ran for almost five months and "My Hero" lasted four months. While the shows have proven popular, they have also earned many complaints from people who say they are crude and not satisfactory.

1. It can be inferred from the passage that _______.

A. Male applicants from Hong Kong won’t be accepted to attend Happy Boy show.

B. It was Hunan TV that made the regulation that they couldn’t accept foreign applicants.

C. American Idol was started earlier than Super Girl.

D. Audience love American Idol better than Happy Boy.

2. Which of the following may best explain the underlined word spoiled in paragraph 3?

A. prevented       B. gave       C. encouraged        D. affected

3. We can safely draw the conclusion that ________.

A. Hunan TV will obey the regulations issued by the administration.

B. not all of the audience think highly of the shows.

C. there were about 10 popular TV shows across the country.

D. Dragon TV broke the regulations on purpose.

4. The relationship between State Administration of Radio, Film and Television and Hunan TV is possibly close to _______.

A. teacher and student                     B. coach and sportsmen

C. father and son                              D. police and criminal