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4-masalada chiziqsiz programmalash masalalari;

5-masalada qavariq programmalash masalalari berilgan.


Tuzuvchilar: B.T. Egamberdiyev – dotsent.

F.R.Rizayev – MN-53 guruh talabasi

VARIANT – 1
1. Quyidagi shartlar bilan berilgan masalani ikkilangan masalaga keltiring va yeching.




2. Quyidagi transport masalasining boshlang’ich yechimini “shimoliy-g’arb burchak” usuli bilan toping va yeching.

bj ai	80	120	70	130
100	10	7	16	8
150	6	8	13	11
150	8	10	12	5

3. Berilgan butun sonli programmalash masalasini grafik usulda yeching.

, - butun

4. Quyidagi



shartlarni qanoatlantiruvchi funksiyaning maksimum va minimum qiymatini toping va yeching.
5. Quyidagi kvadratik programmalash masalasining yechimlarini Kun—Takker teoremasining shartlaridan foydalanib toping va yeching.




VARIANT – 2
1. Quyidagi shartlarda funksiyaning maksimum qiymatini toping va yeching.


2. Berilgan transport masalasining boshlang’ich yechimini “minimal harajatlar” usuli bilan toping va yeching.

bj ai	80	120	70	130
100	6	5	4	8
250	7	10	11	7
200	6	5	3	9

3. Berilgan butun sonli programmalash masalasini grafik usulda yeching.

, - butun

4. Quyidagi shartlarni qanoatlantiruvchi funksiyaning maksimum qiymatini toping va yeching.





5. Quyidagi kvadratik programmalash masalasining yechimlarini Kun—Takker teoremasining shartlaridan foydalanib toping va yeching.


,


VARIANT – 3
1. Quyidagi shartlarda funksiyaning minimum qiymatini toping va yeching.


2. Berilgan transport masalasining optimal yechimini potensiallar usuli bilan toping va yeching.

bj ai	50	50	50	50
34	2	7	6	4
46	1	7	5	8
60	10	2	8	11
60	7	7	5	5

3. Quyidagi chiziqli programmalash masalasining butun sonli yechimini toping va yeching.

, - butun

4. Quyidagi




shartlarni qanoatlantiruvchi funksiyaning maksimum qiymatini toping va yeching.

5. Quyidagi


shartlarda funksiyaning maksimum qiymatini toping va yeching.

VARIANT – 4
1. Quyidagi masalani chiziqli programmalashning ikkilangan masalasiga keltiring va ikkilangan simpleks usul bilan yeching:



2. Quyidagi masalani – usul bilan yeching.

bj ai	10	40	40	10
20	5	7	8	10
30	11	9	7	6
50	5	3	5	4

3. Masalaning butun sonli optimal yechimini toping va yeching.

, , - butun

4. Quyidagi



shartlarni qanoatlantiruvchi funksiyaning maksimum qiymatini toping va yeching.

5. Quyidagi kvadratik programmalash masalasining yechimlarini Kun—Takker teoremasining shartlaridan foydalanib toping va yeching.



,

VARIANT – 5
1. Quyidagi masalani chiziqli programmalashning ikkilangan masalasiga keltiring va ikkilangan simpleks usul bilan yeching:



2. Quyidagi ochiq modelli transport masalalarini yeching.

bj ai	250	250	250	200
400	7	5	8	11
300	10	6	5	3
300	2	7	3	4

3. Masalaning butun sonli yechimini toping va yeching.

, - butun

4. Quyidagi



shartlarni qanoatlantiruvchi funksiyaning maksimum qiymatini toping va yeching.
5. Kun-Takker shartlaridan foydalanib, X°= (1;0) nuqta quyidagi chiziqsiz programmalash masalasining yechimi ekanligini ko'rsating:


,

VARIANT – 6
1. Quyidagi masalani chiziqli programmalashning ikkilangan masalasiga keltiring va ikkilangan simpleks usul bilan yeching:



2. Quyidagi ochiq modelli transport masalalarini yeching.

bj ai	180	170	150	150
100	5	7	6	3
130	3	5	4	7
150	7	6	3	2

3. Berilgan butun sonli programmalash masalasini grafik usulda yeching.

, - butun

4. Quyidagi

shartlarni qanoatlantiruvchi funksiyaning maksimum qiymatini toping va yeching.
5. Kun-Takker teoremasining shartlaridan foydalanib, x°(0,8; 0,4) nuqta quyidagi qavariq programmalash masalasining yechimi ekanligini ko'rsating:

,

VARIANT – 7
1. Quyidagi masalani chiziqli programmalashning ikkilangan masalasiga keltiring va ikkilangan simpleks usul bilan yeching:



2. Berilgan transport masalaning boshlang’ich tayanch yechimini toping va yeching.

bj ai	150	150	100
200	1	3	4
150	4	3	1
50	3	1	4

3. Berilgan butun sonli programmalash masalasini grafik usulda yeching.

, - butun


4. Quyidagi

shartlarni qanoatlantiruvchi funksiyaning maksimum qiymatini toping va yeching.
5. Quyidagi kvadratik programmalash masalasining yechimlarini Kun—Takker teoremasining shartlaridan foydalanib toping va yeching.



,


VARIANT – 8
1. Quyidagi masalani chiziqli programmalashning ikkilangan masalasiga keltiring va ikkilangan simpleks usul bilan yeching:




2. Berilgan transport masalaning boshlang’ich tayanch yechimini toping va yeching.

bj ai	120	80	50
130	1	7	8
70	6	1	1
50	7	6	1

3. Berilgan butun sonli programmalash masalasini grafik usulda yeching.

, - butun

4. Quyidagi


shartlar bajarilganda funksiyaning shartli ekstremumga ega bo’lgan nuqtasini toping va yeching.
5. Quyidagi kvadratik programmalash masalasining yechimlarini Kun—Takker teoremasining shartlaridan foydalanib toping va yeching.



VARIANT – 9
1. Quyidagi masalani chiziqli programmalashning ikkilangan masalasiga keltiring va ikkilangan simpleks usul bilan yeching:



2. Berilgan transport masalaning boshlang’ich tayanch yechimini toping va yeching.

bj ai	70	70	70
110	1	3	3
70	3	1	3
30	5	3	4

3. Berilgan butun sonli programmalash masalasini grafik usulda yeching.

, - butun

4. Quyidagi masalada Lagranj usulini qo'llab statsionar nuqtalarni toping va shartli ekstremumlarni aniqlang va yeching.
bo’lganda.

5. Quyidagi qavariq programmalash masalalarini yeching.


,


VARIANT – 10
1. Quyidagi masalani chiziqli programmalashning ikkilangan masalasiga keltiring va ikkilangan simpleks usul bilan yeching:



2. Berilgan transport masalaning boshlang’ich tayanch yechimini toping va yeching.

bj ai	150	100	100	150
120	8	6	1	4
180	1	8	6	7
200	6	8	4	2

3. Berilgan butun sonli masalani R.Gomori usuli bilan yeching.

, - butun

4. Quyidagi masalada Lagranj usulini qo'llab statsionar nuqtalarni toping va shartli ekstremumlarni aniqlang va yeching.


bo’lganda.
5. Quyidagi qavariq programmalash masalalarini yeching.


,



VARIANT – 11
1. Quyidagi masalani chiziqli programmalashning ikkilangan masalasiga keltiring va ikkilangan simpleks usul bilan yeching:



2. Berilgan masalaning optimal yechimini toping va yeching.

bj ai	30	50	70
45	7	4	5
45	5	7	4
60	4	5	8

3. Berilgan butun sonli masalani R.Gomori usuli bilan yeching.

, - butun

4. Quyidagi masalada Lagranj usulini qo'llab statsionar nuqtalarni toping va shartli ekstremumlarni aniqlang va yeching.
sohada
5. Quyidagi kvadratik programmalash masalasining yechimlarini Kun—Takker teoremasining shartlaridan foydalanib toping va yeching.





VARIANT – 12
1. Quyidagi shartlar bo’yicha masalani ikkilangan masalaga keltiring va ikkala masalaning yechimlarini toping va yeching.



2. Berilgan masalaning optimal yechimini toping va yeching.

bj ai	100	100	100	100
119	5	3	7	6
121	6	7	5	3
160	3	4	5	6

3. Berilgan butun sonli masalani R.Gomori usuli bilan yeching.

, - butun

4. Quyidagi masalada Lagranj usulini qo'llab statsionar nuqtalarni toping va shartli ekstremumlarni aniqlang va yeching.

sohada bo’lganda.
5. Quyidagi (
, chegara shartlarida funksiyaning maksimum qiymatini toping va yeching.

VARIANT – 13
1. Berilgan masalaga ikkilangan masala tuzing va yeching.


, ,

2. Berilgan masalani – usulini qo’llab yeching.

bj ai	60	60	40	90
50	8	6	5	4
70	3	4	5	6
40	6	7	8	9
90	9	6	5	4

3. Berilgan butun sonli masalani R.Gomori usuli bilan yeching.

, - butun

4. Quyidagi masalada Lagranj usulini qo'llab, shartli ekstremumlarni tekshirib, statsionar nuqtalarni toping va yeching.
bo’lganda.
5. Frank-Vulf usulini qo’llab quyidagi


,
shartlarda funksiyaning maksimum qiymatini toping va yeching.

VARIANT – 14
1. Berilgan masalaga ikkilangan masala tuzing va yeching.


, ,

2. Berilgan masalani – usulini qo’llab yeching.

bj ai	120	90	45	45
110	2	5	3	6
100	5	2	7	9
90	9	6	5	3

3. Quyidagi shartlarda butun sonli masalani yeching:



bu yerda lar butun sonlar.
4. Quyidagi masalada Lagranj usulini qo'llab, shartli ekstremumlarni tekshirib, statsionar nuqtalarni toping va yeching.
bo’lganda.
5. Errou—Gurvits usulini qo'llab, masalani yeching, ya’ni quyidagi chegara shartlarida:
(
,




VARIANT – 15
1. Berilgan masalaga ikkilangan masala tuzing va yeching.


, , ,

2. Berilgan ochiq modelli transport masalasini yeching.

bj ai	35	25	20
20	5	2	3
30	8	6	7
20	2	5	4

3. Quyidagi masalalarning to‘liq butun sonli yechimlarini toping va geometrik izohini (mumkin bo’lgan joyda) bering (bu yerda ):



4. Quyidagi masalani geometrik interpretatsiyadan foydalanib yeching,

,
Z max(min)
5. Gradiyent usullarini qo’llab, quyidagi funksiyalarning berilgan nuqtalardagi gradiyentlarini toping va yeching.
1)
2)
3)
4)
VARIANT – 16
1. Berilgan masalaga ikkilangan masala tuzing va yeching.


,


2. Berilgan ochiq modelli transport masalasini yeching.

bj ai	60	60	60
50	5	7	6
40	6	3	1
110	1	9	11

3. Quyidagi masalalarning to‘liq butun sonli yechimlarini toping va geometrik izohini (mumkin bo’lgan joyda) bering (bu yerda ):



4. Grafik usuldan foydalanib, quyidagi chiziqsiz programmalash masalasini yeching.

5. Frank-Vulf usulini qo’llab boshlang’ich nuqtasi X⁽⁰⁾ = (2;2) bo’lganda quyidagi


,
shartlarda F funksiyaning maksimum qiymatini toping va yeching.


VARIANT – 17
1. Berilgan masalaga ikkilangan masala tuzing va yeching.


,

2. Berilgan ochiq modelli transport masalasini yeching.

bj ai	100	110	120	90
115	9	8	10	11
125	11	10	9	8
160	3	7	5	6

3. Quyidagi masalalarning to‘liq butun sonli yechimlarini toping va geometrik izohini (mumkin bo’lgan joyda) bering (bu yerda ):



4. Grafik usul bilan quyidagi masalani yeching va Kun-Takker shartlarining bajarilishini tekshiring va yeching.


,
Z
5. Jarima funksiyasi va Errou-Gurvits usulini qo’llab, quyidagi


,
shartlarda F funksiyaning maksimum qiymatini toping va yeching.

VARIANT – 18
1. Berilgan masalaga ikkilangan masala tuzing va yeching.


, , , ,

2. Berilgan ochiq modelli transport masalasini yeching.

bj ai	90	90	90	90
100	2	7	9	10
120	3	3	6	8
180	4	2	7	4

3. Quyidagi masalalarning to‘liq butun sonli yechimlarini toping va geometrik izohini (mumkin bo’lgan joyda) bering (bu yerda ):



4. Kun-Takker shartlaridan foydalanib X⁽⁰⁾ = (1; 0) nuqta quyidagi chiziqsiz programmalash masalasining yechimi ekanligini ko’rsating va yeching.

,
Z
5. Quyidagi


shartlarda funksiyaning maksimum qiymatini toping va yeching.

VARIANT – 19
1. Berilgan masala va unga ikkilangan masalaning yechimini toping va yeching.

)


2. Berilgan transport masalaning boshlang’ich yechimini “minimal harajatlar” usuli bilan toping va yeching.

		Iste’molchilarning mahsulotga bo’lgan talabi
		200	200	100	100	250
Taminotchilardagi mahsulot hajmi	100	10	7	4	1	4
	250	2	7	10	6	11
	200	8	5	3	2	2
	300	11	8	12	16	13

3. Quyidagi masalalarning to‘liq butun sonli yechimlarini toping va geometrik izohini (mumkin bo’lgan joyda) bering (bu yerda ):



4. Quyidagi masalani grafik usulda yeching va yechim Kun-Takker shartlarini qanoatlantirishini tekshiring va yeching.

,
Z
5. Quyidagi kvadratik formaning ko'rinishi aniqlansin:


VARIANT – 20
1. Masalaga ikkilangan masalani tuzing va ikkala masalaning optimal yechimini toping va yeching.


, ,

2. Berilgan transport masalaning boshlang’ich tayanch yechimini toping.

bj ai	120	80	50
130	1	7	8
70	6	1	1
50	7	6	1

3. Quyidagi masalalarning to‘liq butun sonli yechimlarini toping va geometrik izohini (mumkin bo’lgan joyda) bering (bu yerda ):



4. Quyidagi qavariq pragrammalash masalasining boshlang’ich yechimi berilgan holda gradient usul bilan optimal yechimi toping va yeching.

, ,


Z_min

5. Quyidagi kvadratik programmalash masalasining yechimlarini Kun—Takker teoremasining shartlaridan foydalanib toping va yeching.



,


MUNDARIJA

	Variantlar	Bet
	1-variant ..………………………………………………………...………………	3
	2-variant ..………………………………………………………...………………	4
	3-variant ..………………………………………………………...………………	5
	4-variant ..………………………………………………………...………………	6
	5-variant ..………………………………………………………...………………	7
	6-variant ..………………………………………………………...………………	8
	7-variant ..………………………………………………………...………………	9
	8-variant ..………………………………………………………...………………	10
	9-variant ..………………………………………………………...………………	11
	10-variant ..……………………..………………………………...………………	12
	11-variant ..…..…………………………………………………...………………	13
	12-variant ..…..…………………………………………………...………………	14
	13-variant ..…..…………………………………………………...………………	15
	14-variant ..…..…………………………………………………...………………	16
	15-variant ..…..…………………………………………………...………………	17
	16-variant ..…..…………………………………………………...………………	18
	17-variant ..…..…………………………………………………...………………	19
	18-variant ..…..…………………………………………………...………………	20
	19-variant ..…..…………………………………………………...………………	21
	20-variant ..…..…………………………………………………...………………	22