maths question~F.3, urgent

let X be the number of Apple
let Y be the number of Orange
then 2X+1.5Y <= 65, also X >=0, Y >= 0
a)
For Max. no.
By plotting the inequality diagram, X=1 and Y=42 for X>0 and Y>0
maximum no. of fruit is also 43
For Min. no.
By plotting the inequality diagram, X=31 and Y=2 for X>0 and Y>0
minimum no. of fruit is 33

b) for X>=5 and Y>=5
By plotting the inequality diagram,
max. no. of fruit is X=6 and Y=35, total 41
or X=5, Y=36, also give total 41

By plotting the inequality diagram
min no. of fruit is X=28 and Y=6, total 34


2008-09-09 22:53:00 補充：
強制同假定, 只會出現在大學問題. 中小學問題毛需要出現

中小學問題當然毛需理會! 小學生應該也懂這個 原理!

(沒有人說過 Dicky 一定要把錢用掉, 那就是說, 他可以不買任何水果, 所以他最少可以買 0 個水果, 我估計出題者是希望您回答 32 這個數, 但很遺憾, 他的題目有很大的問題, 所以 0 才應該是真正的答案), 聽 起來, 相當有道理!

如果這是 IQ題, 我必然同意 (所以 0 才應該是真正的答案).

但是, 這不是 IQ題!

(a) The number of fruits Dicky can buy is maximum if he only buys apple

65/1.5 = 43 with a remaining of $0.5
Therefore, the maximum number of fruits Dicky can buy is 43.

(要留意, 題目沒有說一定要把 $65 都花光, 所以第一位回答者的計算方法是不正確的, 但這裡因為 $65 可以買 42個蘋果及 1 個橙, 所以答案才會跟我的方法一樣)

If you follow a similar way of thinking as shown above,

The number of fruits Dicky can buy is minimum if he only buys oranges
65/2 = 32 with a remaining of $1

Therefore, the minimum number of fruits Dicky can buy is 32.

(同樣地, 題目沒有說一定要把 $65 都花光, 所以第一位回答者的計算方法是不正確的)

However, the above idea of minimum number of fruits he can buy is not quite true. The condition here is that Dicky has $65. It does say that Dicky has to spend the money. If Dicky does not spend the money, that will imply that he cannot buy even one fruit. As a result, the minimum number of fruits he can buy should be 0.

(解釋一下, 沒有人說過 Dicky 一定要把錢用掉, 那就是說, 他可以不買任何水果, 所以他最少可以買 0 個水果, 我估計出題者是希望您回答 32 這個數, 但很遺憾, 他的題目有很大的問題, 所以 0 才應該是真正的答案)

(b) Cost of five apples and five orange = $1.5 x 5 + $2 x 5 = $17.5

The number of fruits he can buy will be maximum if he only buy apples using the remained amount of money

(65 - 17.5)/1.5 = 31 with a remaining of $1.

Therefore, the maximum number of fruits he can buy is

31 + 5 + 5 = 41

2008-09-05 20:12:05 補充：
The number of fruits he can buy will be maximum if he only buy apples using the remained amount of money

對唔住, 呢個錯左, 應該係

The number of fruits he can buy will be maximum if he only buy oranges using the remained amount of money