郭日僑華
(a) Write down the constaints of x
and y.
or
x+y ✓ 25
2x+5y < 100
(b) Express Pin terms of x and y.
-2x+y * 40
x > 0
六期星日九月二十(九八九一年八十七國民葦中
X > 0, y > 0
12x+5y > 60
7x+10y70.
x, y are integers
風南斗北 日
find
Y 20
graphically the values of x and
(c)
(ii) The profit is $(11x+18y). (b) (i)
(33)日二十月一十年日己曆夏
1990 中學會考預習專欄
明德出版社-
MILL & DALE PRESS
Mathematics (10)
(a) How many bays of each should be
prepare.
(b) What is the greatest profit?
4. There are two types of buses, A and B for hire. The rent on each bus A is $80, and on each bus B is $60. The capacity of each bus is given by the table below:
(c) On the graph provided,
**
(d) Find the value of P.
Exercise 10 Linear programming
W. K. Lo
Bus A
People
36
Luggage
40-
Solutions
140 kg
1. (a) 100-X + }
30
Bus B
15
200 kg
= 100 - (x-y)
1. (a) Maximize
100-x+y under
the
constraints
x > 2
In
x 10
32
ye
(b) Minimize 100-(x+y) under
constraints.
x: > 3
X < 8
y> 5
there cre school picnic, # altogether 180 students and 1400 kg of luggage. if the most economical way is to hire x bus A and y bus B. (a) Write down the cost in terms of
x and y.
the
10
(b) Write down the constraints for
x and y.
(c) Give
the
solution of the constraints graphically by using the graph provided below.
5
Y
Y 12
X. y are integers.
2. A farmer has 25 acres of land, $1000 capital and 120 man-days of labour to prepare for two crops A and B. The cost per acre for sowing crop A Is $20 and for crop. B is 350. Crop A takes 6 man-days per cre while crop B takes. 3 nan-days per acre. The profit on crop A.is $11 per acre and that on crop # is $18 per acre. The farmer speet x acre for crop A and y acre for crop. 8.
(a)(i) Write down the constraints in terms of x and y.
(ii) Write down the profit in
terms of x and y.
(bUsing the graph provided below,
find
(1) the values of x and y if he
wants to have maximum profit. (ii) the maximum profit.
30
20-
10
20
30
40%
104
(d) What are the values of x and y?
(e) What is the cost?
Pach
5. The following table gives the amount f
of Vitamins A, kilogramme(kg) of food
Vitamin A Vitamin B Vitamin C
Food X
3
10
Food Y
5
The minimum amount of Vitamins A, 8 and C required per week arc
(6.5,16.5)
20-
10
10
20
30
10-
y=2
From the graph,
x = 8.5
y = 16.5 (Note: Accurate calculation
gives x = y = 16)
(d) From the graph,
x=3, y=6
(Ans.)
(e) The cost
10
19 x
(ii) The maximum profit.
= 80(3) + 60(6) = $600
{Ans.)
The minimum value of x-y under
= 11(8.5) + 18(16.5) = $390.5
(Ans.)
the constraints
# (2) - (8)
-5
The maximum value of 100-(x-y)
3. (a) Let x bags of X and y bags of Y
are prepared.
5. (a) The constraints are
x % 0
is given by
Profit = $(50x+30y)
100(-6)
= 106
(Ans.)
The constraints are
2x+4y < 50 4x+2y401 6x+5y 75
X > 0 y 20
y are integers.
y >
x+3y > 12
X+ 8
2x+y > 12
(b) P = 10x + 20y
= 10(x+2y)
y > 0 4x+12у 48 3x+3y24 10x+5y > 50
or simply
X X 0
Than
IWU
of
3. A
prepares
types Fertilizer X and Y. Each bag of X contains 2 kg of chemical A, 4 kg of chemical B and 6 kg of chemical C. Each bay of Y. contains 4 kg of chemical A, 2 kg of chemical B and 5 kg of chemical C. Each bag of X yields a profit of $50 and each bag of Y yields a profit of $30. arcant of chemicals available 50 kg of A, 40 kg of B and 75 kg. of
C.
The
15
Vitamin A
tamin B
Vitamin C
48
24
60
The cost of food X and Y are $10 per kg and $20 per kg respectively. If obtain the the cheapest way to intake is to take kg of food X and 3 kg of food per week and the cost is $P.
1990 中學會考預習專攔
Computer (10)
明出版社
MILL & DALE PRESS
The relationship between flowchart and BASIC.
(a) Sequence
2.g.
START
Program Segment
elestion
10
The maximum value of (x+y) under
the constraints
= (7) + (11) = 18
The minimum value of 100~(x+y). under the constraints
10
From the graph, x-7 and y=6.
... 7 bags of X and 6 bags of Y
should be prepared.
(Ans.)
100 - (18)
= 82
2. (a)
(i)
x+y< 25 20x+50y 1000
6x+3y $120
X 2.0
Y Q
PU
K. Choy
M
N - 4 + 2
(b) Profit
(Ans:)
= 7(50) + 6(30) →→ $530
(c)
18
10-
10x+20y=100;
16,21
衲呢?也就有特高明作袿論了。 。能不能說他是一节西点华丽的憍笛 僑附熱,但是,佔澤西行的資料似乎更多 前已有華人僑居海外,而徐福是第一位華
多不方安啊! + 亦不會有問題的,袋署全部東西出入,
個多月來的孤獨感受,一掃而空。 聖誕節的婓件-使室內美觀極了。把我兩 REUZEREK, BECH:54
毋都甚理想,美滿,只可做水喉結
,水流不出來,只有採用火攻的方法
·我也去公司班
血,稍低至兩折三折呢,所以有很多人際
(Ans.)
聲傳市
10 11 12 x
From
the graph, the optimal
solution is (6, 2)
4. (a) Cost = ${80x +
(b)
x > 0, y 2.
36x+15y 180
140x+200у 1400
are integers
Soy)
(Ans.)
* ༢ f
y 2
(Ans.)
(d) P 10(6) + (20)(2)
100
{Ans.)
NEXT 1
BASIC statement
100
REM BODY OF BUBBLE SORT
110
FOR J = 1 TO 19
120
FOR K = 1 TO-20 - J
> 0 THEY M + 1 ELSE
130
N + 2
140
150
160
.170
180
NEXT J
200
210
PRINT "THE SORTED LIST:"
220
FOR 1 TO 20
230
IF MARK(K) > MARK (K+1) THEN 170
NEXT K
TNAMES= NAMES(K) TEMP MARK(K)
NAMES(K) = NAMES(K+1) MARK(K) = MARK(K+1) NAMES(K+1)= TNAMES: MARK{K+1)= TEMP
REM PRINT THE SORTED LIST IN ORDER OF MARK
PRINT NAMES(1), MARK(1)
240
NEXT I
250 END
(d) Implementation of Counter
BASIC segment
START
INPUT sumber, X
10 INPUT "PLEASE INPUT A NUMBER "H
t = 1
10 FOR I = 1 TO 40 STEP 1
X
Y Xi
20 LET Y XA2
!NPUT
20 INPUT MARK
MARK
PRINT Y
30 PRINT "THE SQUARC OF THE
NUMBER IS" Y
30 NEXT !
SOP
40 END
Discussion:
(1) REM statements should be added whenever appropriate.
description of the following program segment is written.
The job
(2) Structural programming is a good practice. Do not use too much GOTO statements. Otherwise you may get lost in the program statements. Identation of the program makes it clear that it is a loop.
e.g.
-110
FOR 1 TO 19
120
FOR K 1 TO 20 - 3
170
180
- NEXT K NEXT J
此等引術問題,等到接任之「不幸」者,看上宮服
標 知其科生滿诚者,於是想脫;來不及矣!
秘
張庭
(b) Unconditional Branching and Conditional Branching:
4.4.
Program Segmerit
IS
40
(e) Subroutine
START
BASIC statement
10. GOSUB 500
20
PUT
"radius"
10 INPUT "PLEASE INPUT THE
RADIUS OF CIRCLE"; R
Sorting the number in assecoding
order
500 REM BUBBLE SORT 510
20 IF R 0 THEN 60
590 RETURN
Yea
5
STOP
AREA
Programming Exercise
3.1416 x R2
30 AREA - 3.1416 R2
1. Bubble sort
Write a program in BASIC that can do the following jobs.
MAREA", AREA
40 PRINT "AREA OF CIRCLE = ";
AREA
(a) A list of 20 names and marks are input into a
dimensional array.
two-
50 GOTO 10
60 END
(b) The list of names and marks are sorted according to the
decending order of marks.
The structure make it easy that lines between 120 and 170 is the inner loop and lines between 110 and 180 is the outer loop. No inter-crossing of loop will happen. But it is only true for most versions of BASIC but not for APPLE II user unless a set of machine code is keyed in. You are requested to use structural programming style when answering questions in the HKCEE.
(3) For students using the Commodore PC-10 model of computer. Lines
140 to 160 can be replaced by
you
140 SWAP NAMES(X), NAME${X+1) 150 SWAP MARK(K), MARK(K+1)
The SWAP function exchanges the values of two variables. However
this functionin suggested not to use are examination because it is not included in the reserved work list You are announced by the Hong Kong Examination Authority. encourage to use a wide variety of functions provided by your machine in the computer laboratory but not in the examination.
2. Using the sorted list of the student names and marks in (1). Write a subroutine program using the algorithm of linear search to look for the existence of a student and then print his mark. and position.
500
REM SUBROUTINE: LINEAR SEARCH
510
(c) The sorted list should be printed out.
520
FOR 1.1 TO 20
530
BASIC program
540
Remarks:
(1) Box 3 is the conditional branching, the branching depends on the radius as the condition. Line 20 is the corresponding BASIC statement.
10 REM INPUT OF NAMES AND MARKS
550
PRINT "MARK": MARK(I)
20 DIM NAMES(20), MARK(20)
560
30
FOR I = 1 TO 20
570
GOTO 660
40
(2) The Flowline after box 5 is the unconditional branching. Line!
50 is the corresponding BASIC statement.
50
INPUT "NAME OF STUDENT"; NAMES(1) INPUT "MARK OF STUDENT"; MARK(1)
580
NEXT I
590.
INPUT "NAME OF STUDENT TO BE SEARCH": NAS
IF NAS NAMES(I) THEN 580
PRINT "NAME OF STUDENT"; NAME$(1)
PRINT "POSITION": 1
PRINT "THE STUDENT IS NOT IN THE LIST!"
揉說卹
慈買一件大碼 然大受男人 雖然买人服 睇]·组睫 一些。
60
660
EMD