rose_1126

A machine shop produces propellers and gear systems for boats.It takes about 2h to make a propeller and 3h for a gear system.A regulation on noise pollution limits machine operation to 98h per week. The space set aside for storage is 200M3. A box containing a propeller occupies a volume of 1M3 and a gear system needs 3M3. A market survey concludes that the shop must make at least twice as many propellers as gear systems. If a propeller sells for $40 and a gear system for $60,find the maximum revenue.

a) What are the two variables in this examples?

b) Find the equation of the function rule.

c)State the system of inequalities that describes the constraints of the problem, then graph the system.

d) Find the number of propellers and the number of gear system tha tthe shop should make to earn maximun revenue.

e)HOw much is this revenue?

因为孩子要完成作业，本人看英文有困难，不理解题意，估计是用方程式，请热心人帮忙解答。请发邮件renbing_1126@yahoo.com.cn    谢谢

rita0608

answer is 7800$?
the key point is the revenue. wheter it is weekly,monthly or yearly

rchen_mtl

a) X, number of propellers produced; Y, number of gear produced
b) max = max(40X + 60Y)
c) 2X+3Y=98
   X + 3Y <=200
   X >= 2Y
d) X = 28 Y = 14
e) max = 1960

HawkX

原来这里的小孩做这么好玩的题目，来凑个热闹。其实3楼的基本上做对了，我稍微写详细一点，再加上一点修正。
我的英文也有点不够用：the shop must make at least twice as many propellers as gear systems，搞不清是哪个要是哪个的两倍以上，但由于这个题目凑准了数字，所以这个条件限制不影响maximun revenue结果。
X为propeller个数，Y为gear个数。
1)   2X+3Y<=98
2)   X+3Y<=200
3)   X>=2Y还是Y>=2X
4)   X>0
5)   Y>0
求40X+60Y的最大值。
坐标系里画个图，发现1)、4)、5)满足（第一象限的一个直角三角形）的话，2)自动满足。巧的是1)当中2X+3Y的比例和待求的40X+60Y比例一样，3)就扔掉拉倒，1)放大20倍得到40X+60Y<=1960.
要答对问题d)，必须搞清楚3到底是那个倍数关系。但无论是哪一种，这个题目本身都点问题：在maximun revenue处对应的X和Y其实没有唯一解。

我学数学的时候，国内对不等式画图不是很重视。看了这个题目，联想自己在这里的学习，觉得老外对数学在现实生活中的实际意义比较重视，这一点要比中国强。

好了，我该去补习英语了。

sino000

QUOTE=HawkX]

X为propeller个数，Y为gear个数。
1) 2X+3Y<=98
2) X+3Y<=200
3) X>=2Y
4) X>0
5) Y>0
求40X+60Y的最大值。
[/QUOTE]

rose_1126

感谢朋友的帮忙,真正感到了祖国的温暖,再次感谢

rose_1126

能请您留个电话或者邮箱吗?我想就坐标图再请教您,谢谢

Post by sino000
QUOTE=HawkX]

X为propeller个数，Y为gear个数。
1) 2X+3Y<=98
2) X+3Y<=200
3) X>=2Y
4) X>0
5) Y>0
求40X+60Y的最大值。

[/QUOTE]

rita0608

我认为这题有问题,你的答案28,14不对.你看40,6也符合所有条件,但取得的收入更高.

HawkX

Post by rita0608
我认为这题有问题,你的答案28,14不对.你看40,6也符合所有条件,但取得的收入更高.

题是有问题，我在4楼说过了：没有唯一解。
直线2X+3Y=98上(28,14)和(49,0)之间随便哪一点都可以，(40,6)就是其中一个。
不过maximum revenue确定就是1960。

sino000

No. There is a unique solution to this problem conditioned on the maximal revenue, which can only be achieved with the largest Y.

That means the larger Y, the larger the revenue. The maximal revenue corresponds to the largest value of Y, which is located at the top in the green shadow area.

It should be pointed out that each point in the green area, including the three edges of the triangle, satisfies all the conditions except for the maximal revenue condition, which can only be satisfied by the top point corresponding to the unique solution.

Post by HawkX
题是有问题，我在三楼说过了：没有唯一解。
直线2X+3Y=98上(28,14)和(49,0)之间随便哪一点都可以，(40,6)就是其中一个。
不过maximum revenue确定就是1960。