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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 1
wWw.Kenhdaihoc.com Knh thng tin Hc tp Gii tr
Bi 1:
Phn
xng
Nng sut lao ng
m/cng nhn
Sn lng
(mt) i
i
x
M
A 40 1200 30
B 45 2025 45
C 50 1600 40
4825 115
Tnh nng sut lao ng bnh qun ca cng nhn cc phn xng.
Gii:
ix : nng sut lao ng (m/cng nhn) iM : Sn lng (mt)
i
i
x
M: s cng nhn
95,41115
4825
x
M
Mx
i
i (m/cng nhn)
Bi 2 ( Bi tp 7 P198 )
Di y l ti liu phn t theo khi lng c nh c ca mi thuyn trong on thuyn
nh c.
Khi lng c (t) S thuyn Tng lng c ii fx
Di 25 5 12.5 62.5
25 50 13 37.5 487.5
50 75 16 64.5 1032
75 100 8 87.5 700
100 125 6 112.5 675
48 2925
a. Tnh s trung bnh c nh c ca mi thuyn.
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 2
b. Tnh trung v, mt v khi lng c nh c ca mi thuyn
c. So snh kt qu cu a v cu b v cho nhn xt v phn phi ca dy s.
Gii:
a. ix : Tng lng c if : S thuyn
94.6048
2925
i
ii
f
fxx (t/thuyn)
b.
82.56816.1316
13162550
. 11
1
min
0000
00
00
MMMM
MM
MMoffff
ffhxM (t)
Bi 3:
Phn
xng
Nng sut
lao ng
(SP/CN
S cng
nhn
% hon
thnh k
hoch
Gi thnh
1sp (triu
ng)
Sn
lng
ii fx
'
'
i
i
x
M ii
fx ""
A 40 40 98 2.0 1600 1632.6 3200
B 35 50 102 2.2 1750 1715.6 3850
C 50 60 104 1.8 3000 2884.6 5400
D 40 50 100 2.0 2000 2000 4000
2000 8350 8232.8 16450
1. Hy tnh nng sut lao ng ca cng nhn cc phn xng
2. Hy tnh % hon thnh k hoch ca cc phn xng
3. Hy tnh gi thnh bnh qun ca gi thnh sn phm
Gii:
1. 75.41200
8350
i
ii
f
fxx (sp/cn)
2. 014.18.8232
8350
'
'
''
i
i
i
x
M
Mx (%)
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 3
3. 97.18350
16450
"
".""
i
ii
f
fxx
Bi 4:
C 3 cng nhn cng sn xut mt loi sn phm trong 8 gi. Ngi th 1 sn xut 1 sn phm
ht 8 pht. Ngi th 2 sn xut 1 sn phm ht 10 pht. Ngi th 3 sn xut 1 sn phm ht 6
pht. Hy tnh thi gian hao ph bnh qun sn xut 1 sn phm ca 3 ngi cng nhn ni
trn.
Gii:
59,7
6
1
10
1
8
1
3
6
60.8
10
60.8
8
60.8
60.860.860.8
i
i
i
x
M
Mx (pht/sp)
Bi 5:
Cho s liu thng k 3 phn xng ca 1 doanh nghip nh sau:
Phn xng Nng sut lao ng
(SP/ngi)
S sn phm
(sn phm)
Gi thnh 1 sn phm
(triu ng)
A 20 200 20
B 22 242 19
C 24 360 18
802 36
1. Tnh nng sut lao ng bnh qun chung cho 3 phn xng
2. Tnh gi thnh n v sn phm bnh qun chung cho 3 phn xng trn.
3. So snh phn tn gia nng sut lao ng v gi thnh n v sn phm.
Gii:
1.
i
i
f
M
CN
SPNSLD
278.2236
802
24
366
22
242
20
200
8021
i
i
i
x
M
Mx (sp/cn)
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 4
2.
'
'
i
i
f
M
SP
CPSXGT
8.18802
15078
802
360.18242.19200.20
'
''.2
i
ii
f
fxx (triu ng/sp)
3. 1001
11 x
xVVNSLD
1002
22 x
xVVGT
Trong : 1x = 22.278 (sp/cn)
2x = 18.800 (triu ng/sp)
i
ii
i
ii
f
fx
f
fx22
11
ix : nng sut lao ng tng phn xng
if : s cng nhn tng phn xng
69.2278.2236
24.36022.24220.200 21
(sp/cn)
22
2
22'
''
'
''
i
ii
i
ii
f
fx
f
fx
'ix : gi thnh tng sn phm
'if : s sn phm
677.0800.18802
360.18242.19200.20 2222
2
(triu ng )
Bi 6:
C s liu ca mt doanh nghip nh sau:
Chi ph qung
co (triu ng)
Doanh thu
triu ng xy 2x
2y
2 520 1040 4 270400
4 540 2160 16 291600
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 5
5 590 2950 25 348100
6 610 3660 36 372100
8 630 5040 64 396900
10 640 6400 100 409600
3530 21250 245 2088700
1. Hy xy dng phng trnh hi quy tuyn tnh biu din nh hng ca chi ph qung
co ti doanh thu v gii thch cc ngha tham s.
2. Hy nh gi mc cht ch ca mi lin h gia qung co v doanh thu.
Gii:
1. Phng trnh hi quy tuyn tnh c dng: xbbyx 10
x : chi ph qung co
y : doanh thu
xy
: gi tr iu chnh ca doanh thu
2
10
10
..
.
xbxbxy
xbbny=>
245.35.21250
35..63530
10
10
bb
bb
29.4946
35.12.16
6
3530
12.16
6
35
6
245
6
3530.
6
35
6
21250
.
10
221
xbyb
yxxyb
x
- 0b = 494.29 phn nh nh hng ca tt c cc nguyn nhn khc ti doanh thu.
- 1b = 16.12 phn nh nh hng trc tip ca chi ph qung co ti doanh thu. C
th khi chi ph qung co tng thm 1 triu ng th lm cho doanh thu tng bnh
qun 16.12 triu ng.
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 6
2. 945.0
6
3530
6
2088700
6
35
6
245
2
2
22
22
11
n
y
n
y
n
x
n
x
bbry
x
Bi 7 (Bi 3 - trang 410 )
C d liu v mc tiu th ca mt nhm mt hng ca Cng ty X ti mt th trng nh sau:
Mt hng
Doanh thu T l % tng,
gim gi %
0
1
p
pip
Qu I 00qp Qu II 11qp
A 360000 370500 -2.5 97.5
B 393000 404880 -3.6 96.4
C 177000 189400 -5.3 94.7
930000 964780
1. Tnh ch s tng hp gi theo cc cng thc ch s Laspeyres v ch s Passche.
2. Tnh ch s tng hp lng hng tiu th theo cc cng thc ch s Laspeyres v ch s
Passche.
3. Vi gi nh lng hng tiu th c nh k nghin cu, hy xc nh mc tng (gim)
doanh thu do nh hng bin ng gi bn cc mt hng qu II so vi qu I.
Gii:
1. 965.0930000
897471
930000
177000.947.0393000.964.0360000.975.0.
00
00
00
01
qp
qpi
qp
qpI
pL
p
(ln) hay 96.5 %
965.01000000
964780
947.0
189400
964.0
404880
975.0
370500
964780
11
11
10
11
p
P
p
i
qp
qp
qp
qpI (ln)
hay 96.5%
2. 075.1930000
1000000
00
10
qp
qpI Lq (ln) hay 107.5 %
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 7
075.1897471
964780
01
11
qp
qpI Pq (ln) hay 107.5 %
3. DTQIDTQII
3522010000009647800011 qpqp (nghn)
4. Nu ct cui cng ca bi khng cho t l % tng hoc gim gi m cho t l % tng
hoc gim lng ca qu II so vi qu I th yu cu s 2 s l:
Mt hng
Doanh thu T l % tng,
gim lng %
0
1
q
qiq
Qu I 00qp Qu II 11qp
A 360000 370500 -2.5 97.5
B 393000 404880 -3.6 96.4
C 177000 189400 -5.3 94.7
930000 964780
1. 075.1930000
1000000
930000
947.0
189400
964.0
404880
975.0
370500.
00
11
00
11
1
0
00
11
qp
i
qp
qp
qpq
q
qp
qpI
qL
p
177000.947.0393000.964.0360000.975.0
964780
.. 00
11
00
0
1
11
10
11
qpi
qp
qpq
q
qp
qp
qpI
p
P
p
075.1897471
964780 (ln) hay 107.5 %
5. Vn dng phng php ch s phn tch bin ng tng doanh thu ca 3 mt hng
qu II so vi qu I do nh hng ca 2 nhn t gi v lng.
- Bc 1: Vit h thng ch s:
00
10
10
11
00
11.
qp
qp
qp
qp
qp
qpI
pq
P
q
P
ppqIII .
(ln. %)
- Bc 2: Tnh bin ng tng i:
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 8
930000
1000000.
1000000
964780
930000
964780
pqI
pq
I 1.037 = 0.965 . 1.075 (ln)
( I 1) 0.037 -0.035 0.075 (ln)
3.7% -3.5% 7.5%
- Bc 3: Tnh bin ng tuyt i:
001000110011 qpqpqpqpqpqppq
pq
34780 = -35220 + 70000 (ln)
- Bc 4: Nhn xt:
Tng doanh thu ca cc mt hng qu II so vi qu I tng 3.7% tng ng 34780
(nghn ng) do nh hng ca 2 nhn t:
o Do gi gim 3.5% lm cho tng doanh thu ca cc mt hng qu II so vi
qu I gim 35220 (nghn ng)
o Do lng tng 7.5% lm cho tng doanh thu ca cc mt hng qu II so
vi qu I tng 70000 (nghn ng).
Bi 8 (bi 4 trang 411)
D liu tng hp v tnh hnh sn xut ca mt x nghip nh sau:
Sn phm
Chi ph sn xut T l % sn
lng thng 2 so
vi thng 1
%0
1
q
qiq
Thng 1 00qz Thng 2 11qz
A 100 104.5 10 110
B 200 230 15 115
300 334.5
1. Xc nh ch s chung v gi thnh sn phm ca doanh nghip (tnh theo quyn s k
gc v k nghin cu)
2. Xc nh ch s chung v sn lng ca doanh nghip (tnh theo quyn s k gc v k
nghin cu)
3. Phn tch s bin ng tng chi ph sn xut bng h thng ch s theo phng php lin
hon.
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 9
Gii:
1. 98.0300
295
300
15.1
230
1.1
5.104.
00
11
00
11
1
0
00
01
qz
i
qz
qz
qzq
q
qz
qzI
p
zq (ln) hay 98%
98.0340
5.334
200.15.1100.1.1
5.334
. 00
11
00
0
1
11
00
11
qzi
qz
qzq
q
qz
qz
qzI
p
z (ln)
2. 13.1300
340
0
10
qz
qzI q (ln)
13.1295
5.334
01
11
qz
qzI q (ln)
3. - Bc 1:
00
10
10
11
00
11.
qz
qz
qz
qz
qz
qzI
zq
qzzqIII .
- Bc 2:
300
340.
340
5.334
300
5.334
zqI
133.1.983.0115.1 zq
I
0.115= -0.017 0.133
11.5% -1.7% 13.3%
- Bc 3:
001000110011 qzqzqzqzqzqzzq
pq
34.5 = -5.5 + 40 (triu ng)
- Bc 4:
Tng doanh thu ca cc mt hng thng 2 so vi thng 1 tng 11.5% tng ng
34.5 triu ng do nh hng ca 2 nhn t:
o Do gi gim 1.7% lm cho tng doanh thu ca cc mt hng thng 2 so
vi thng1 gim 5.5 triu ng.
o Do lng tng 13.3% lm cho tng doanh thu ca cc mt hng thng 2 so
vi thng 1 tng 40 triu ng.
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 10
Bi 9:
C s liu thng k v tnh hnh thu hoch la trong nm 2009 ca cc t hp tc x nh sau:
HTX
V ng xun V h thu
Nng sut (ta/ha) Sn lng (t) Nng sut (ta/ha) Sn lng (t)
A 38 5.510 32 150
B 34 6.290 34 180
C 36 8.640 33 230
x 20.440 x 560
1. Tnh nng sut la trung bnh v ng xun ca cc hp tc x trn
2. Tnh nng sut la trung bnh v h thu ca cc hp tc x trn
3. Tnh nng sut la trung bnh ca mt v trong c nm ca cc hp tc x trn.
Gii
DT
SLNS
i
i
fDT
MSL
:
:
1. 86.35570
440.20
36
640.8
34
290.6
38
510.5
440.20
i
i
i
I
x
M
Mx (t/ha)
2. 05.33560
510.18
560
332303418032150
'
''
xxx
f
fxx
i
ii
II (t/ha)
3. ix" : nng sut thu hoch bnh qun tng v 2,1i
if " : tng din tch tng v 2,1i
47,34130.1
510.18440.20
560570
56005,3357086,35
"
""
xx
f
fxx
i
ii (t/ha)
Bi 10:
C s liu thng k v s sn phm v gi thnh n v sn phm ca cc phn xng nh sau:
S sn phm Gi thnh 1 v xy 2x 2y
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 11
10 20 200 100 400
15 19 285 225 361
20 17 340 400 289
25 15.5 387.5 625 240.25
30 13 390 900 169
100 84.5 1602.5 2250
1. Xy dng phng trnh hi quy tuyn tnh biu hin nh hng ca s sn phm n gi
thnh n v sn phm. Gii thch ngha ca cc tham s trong phng trnh hi quy .
2. nh gi trnh cht ch ca mi lin h gia s sn phm v gi thnh n v sn
phm.
Gii:
1. Tiu thc nguyn nhn: s sn phm (x)
Tiu thc kt qu: gi thnh n v sn phm (y)
Gi phng trnh hi quy tuyn tnh c dng: bxayx
Trong : a v b c xc nh nh sau:
n
xb
n
yxbya
n
x
n
x
n
y
n
x
n
xy
yxxyb
x
222
..
9.235
100)35.0(
5
5.84
35.0
5
100
5
2250
5
5.84.
5
100
5
5.1602
2
a
b
xyx 0359.23
-
PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 12
- a = 23.9 ni ln nh hng ca cc tiu thc nguyn nhn khc n gi thnh n v sn
( tr tiu thc s sn phm ). Nu s sn phm = 0 => 9.23 xy
- b = -0.35 ni ln nh hng ca s sn phm n gi thnh n v sn phm. Khi s sn
phm tng ln mt n v sn phm th gi thnh n v sn phm s gim bnh qun mt
gi tr tng ng l 0.35 (triu ng/sn phm)
2. 99.0
5
5.84
5
25.1459
5
100
5
2250
35.02
2
22
22
2
2
n
y
n
y
n
x
n
x
by
xb
y
xbr
Kt lun: mi lin h gia s sn phm v gi n v sn phm l mi lin h nghch v
rt cht ch.
Bi 11:
Cho s liu thng k v GO ca mt ngnh giai on
Nm GO (t ng) t ty 2t
2004 100 1 100 1
2005 120 2 240 4
2006 135 3 405 9
2007 150 4 600 16
2008 170 5 850 25
2009 200 6 1200 36
875 21 3395 91
1. Xy dng hm xu th tuyn tnh biu din s pht trin v GO
2. Tnh tc tng hoc gim bnh qun v GO trong giai on trn
3. D on GO ca ngnh vo nm 2010 da vo 3 phng n sau:
- D on da vo lng tng tuyt i bnh qun
- D on da vo tc pht trin bnh qun
- D on da vo hm xu th
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PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 13
Gii:
1. Hm xu th tuyn tnh btayt
Trong a v b c xc nh nh sau:
n
tb
n
ytbya
n
t
n
t
n
y
n
t
n
ty
y
yttyb
.
..
222
47.796
21.96.18
6
875
96.1892.2
42.55
6
21
6
91
6
875.
6
21
6
3395
2
a
b
Hm xu th c dng: tyt 96.1847.79
2. 1 ta (ln)
15.01100
2001 51
1
n n
y
ya (ln) hay 15%
3. D on da vo tng hoc gim tuyt i bnh qun: lyy nln .
Trong : 2016
100200
1
1
n
yyn (t ng)
2201202002010 xOG
(t ng)
- D on da vo tc pht trin bnh qun: 2. tyy nln
Trong : 15.1100
20051
1
n n
y
yt (ln)
230)15.1(200 12010 xOG
(t ng)
- D on da vo hm xu th:
19.212796.1847.79 xbtay ln
(t ng)
Bi 12:
C s liu thng k v doanh thu ca 3 mt hng trong 1 doanh nghip nh sau:
-
PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 14
Mt hng Doanh thu (triu ng) T l tng gim
lng III QQ 0
1
q
qiq
Qu I Qu II
A 1000 1200 10 110
B 1100 1350 -5 95
C 1250 1600 8 108
3350 4150
1. Tnh ch s tng hp gi theo cng thc Passche
2. Tnh ch s tng hp lng theo cng thc Laspeyses
3. Vn dng phng php ch s phn tch bin ng tng doanh thu ca cc mt hng
qu 2 so vi qu 1 do nh hng ca 2 nhn t gi v lng.
Gii:
1. 19.1125008.1110095.010001.1
4150
.. 00
11
0
0
1
11
10
11
xxxqpi
qp
qpq
q
qp
qp
qpI
q
P
p (ln)
2. 04.13350
3495
00
10
qp
qpI Lq (ln) hay 104 %
3.
00
10
00
11
00
11.
qp
qp
qp
qp
qp
qpI
pq
L
q
P
ppqIII .
3350
3495.
3495
4150
3350
4150
pqI
pq
I 1.24 = 1.19 x 1.04 (ln)
(I 1) 0.24 0.19 0.04 (ln)
001010110011 qpqpqpqpqpqppq
pq
800 = 655 + 145 ( triu ng )
Nhn xt:
-
PHN BI TP NGUYN L THNG K
Nguyn Th Anh Th K21A-QTKD-HN Page 15
Tng doanh thu ca cc mt hng qu 2 so vi qu 1 tng 24% tng ng tng 800 triu
ng do nh hng ca 2 nhn t:
o Gi tng 19% lm cho tng doanh thu ca cc mt hng qu 2 so vi qu 1 tng
655 triu ng.
o Do lng tng 4% lm cho tng doanh thu ca cc mt hng qu 2 so vi qu 1
tng 145 triu ng.