A shopkeeper sells two brands of cupbroads A and B of volumes 3m^3 and
2m^3 respectively. The cost of each cupboard A is $250 while the cost of
each cupboard B is $200. The shopkeeper decides to buy 8 cupboards A and
some cupboards B.
Suppose that the shopkeeper has 50m^3 space to store the cupboards, and he
can spend at most $3500 to buy the cupboards.
Let x be the number of cupboards B bought.
(a)By considering the storage and the total budget for buying the cupboards,
set up two inequalities in x.
(b)What is the maximum number of cupboards B the shopkeepers can buy?
(c)If the profits made by selling each cupboard A and cupboard B are $150
and $120 respectively, find the maximum total profit he can make.
*Please show the formulas and steps clearly.
(10分)F.2數1題 inequality
2008-03-14 1:10 am
回答 (2)
2008-03-14 2:16 am
✔ 最佳答案
(a)consider the storage
3(8) 2x ≦ 50
x ≦ 13
consider the the total budget
250(8) 200x ≦ 3500
x ≦ 7.5
(b)
since x is a positive integer
∴maximum number of cupboards B is 7
(c)
maximum total profit
=8$150 7$120
=$2040
2008-03-13 18:18:56 補充：
consider the storage
3(8)＋2x≦50
x≦13
consider the the total budget
250(8)＋200x≦3500
x≦7.5
2008-03-13 18:19:24 補充：
maximum total profit
=8$150＋7$120
=$2040
2008-03-13 18:20:24 補充：
maximum total profit
=8($150)＋7($120)
=$2040
≦即是少於或等於
2008-03-14 2:17 am
Give at most can spend $3500, therefore,
8*250+200x ≦3500
2000 + 200x ≦3500
x≦7
Since space available is 50m^3, therefore,
8*3 + 2x ≦50
24+2x ≦50
x≦13
（b）max x=7
（c）8*150+7*120= ﹩2040
2008-03-14 12:40:45 補充：
這網頁未能出到「細過或=」的符號。
&IE 是「少於或等如」的意思。
8*250+200x ≦3500
2000 + 200x ≦3500
x≦7
Since space available is 50m^3, therefore,
8*3 + 2x ≦50
24+2x ≦50
x≦13
（b）max x=7
（c）8*150+7*120= ﹩2040
2008-03-14 12:40:45 補充：
這網頁未能出到「細過或=」的符號。
&IE 是「少於或等如」的意思。
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