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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.



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 (%)



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)



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



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.



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 %



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:



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.



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.



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



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



- 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



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:



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:



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.

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