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CBSE Class 12-science Answered

i don't understaond the transportation problem in example 11of ncert book.plz elaboratly solve it ??
Asked by sweety | 23 Oct, 2015, 09:14: PM
answered-by-expert Expert Answer
H o w space m a n y space u n i t s space s h o u l d space b e space t r a n s p o r t e d space f r o m e a c h space f a c t o r y space t o space e a c h space d e p o t space i n space o r d e r space t h a t space t h e t r a n s p o r t a t i o n space cos t space i s space m i n i m u m. space W h a t space w i l l space b e space t h e space m i n i m u m space t r a s p o r t a t i o n space cos t ?
 
S o l u t i o n colon L e t space apostrophe x apostrophe space b e space t h e space n u m b e r space o f space u n i t s space t r a n s p o r t e d space f r o m space t h e space f a c t o r y space a t space P space t o space t h e space d e p o t space a t space A. A n d L e t space apostrophe y apostrophe space b e space t h e space n u m b e r space o f space u n i t s space t r a n s p o r t e d space f r o m space t h e space f a c t o r y space a t space P space t o space t h e space d e p o t space a t space B. T h e space p r o d u c t i o n space c a p a c i t y space o f space P space i s space 8 space u n i t s. T h u s comma space P space c a n space s e n d space 8 minus x minus y space u n i t s space t o space t h e space d e p o t space a t space C. S i n c e space 8 minus x minus y greater or equal than 0 comma space w e space h a v e comma space x plus y less or equal than 8... left parenthesis 1 right parenthesis N o w space c o n s i d e r space t h e space f a c t o r y space Q. S i n c e space P space i s space s e n d i n g space apostrophe x apostrophe space u n i t s space t o space d e p o t space A space a n d space t h e space r e q u i r e m e n t space o f space A space i s space 5 space u n i t s. T h u s comma space Q space w i l l space s e n d space 5 minus x space u n i t s space t o space d e p o t space A. S i n c e space 5 minus x greater or equal than 0 comma space w e space h a v e comma space x less or equal than 5... left parenthesis 2 right parenthesis S i m i l a r l y comma space P space i s space s e n d i n g space apostrophe y apostrophe space u n i t s space t o space d e p o t space a t space B space a n d space t h e space r e q u i r e m e n t space o f space B space i s space 5 space u n i t s comma a n d space h e n c e comma space Q space w i l l space s e n d space 5 minus y space u n i t s space t o space d e p o t space B. S i n c e space 5 minus y greater or equal than 0 comma space w e space h a v e comma space y less or equal than 5... left parenthesis 3 right parenthesis space T h e space p r o d u c t i o n space c a p a c i t y space o f space t h e space f a c t o r y space Q space i s space 6 space u n i t s. H e n c e space Q space c a n space s e n d space open square brackets 6 minus open parentheses 5 minus x plus 5 minus y close parentheses close square brackets equals x plus y minus 4 space u n i t s space t o space t h e space d e p o t space C. S i n c e space x plus y minus 4 greater or equal than 0 comma space w e space h a v e comma space x plus y greater or equal than 4.... left parenthesis 4 right parenthesis T r a n s p o r t a t i o n space cos t space f r o m space P space t o space A space i s space 160 cross times x. space T r a n s p o r t a t i o n space c o s t space f r o m space P space t o space B space i s space 100 cross times y. T r a n s p o r t a t i o n space c o s t space f r o m space P space t o space C space i s space 150 cross times open parentheses 8 minus x minus y close parentheses space. T r a n s p o r t a t i o n space c o s t space f r o m space Q space t o space A space i s space 100 cross times open parentheses 5 minus x close parentheses. space T r a n s p o r t a t i o n space c o s t space f r o m space P space t o space B space i s space 120 cross times open parentheses 5 minus y close parentheses. T r a n s p o r t a t i o n space c o s t space f r o m space P space t o space C space i s space 100 cross times open parentheses x plus y minus 4 close parentheses space. T h u s comma space t h e space t o t a l space t r a n s p o r t a t i o n space cos t space i s equals 160 x plus 100 y plus 150 open parentheses 8 minus x minus y close parentheses plus 100 open parentheses 5 minus x close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space plus 120 open parentheses 5 minus y close parentheses plus 100 open parentheses x plus y minus 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 10 open parentheses x minus 7 y plus 190 close parentheses O u r space a i m space i s space t o space m i n i m i z e space t h e space t r a n s p o r t a t i o n space cos t. H e n c e space t h e space p r o b l e m space r e d u c e s space t o space M i n i m i z e space Z equals 10 open parentheses x minus 7 y plus 190 close parentheses s u b j e c t space t o space t h e space c o n s t r a i n t s space x greater or equal than 0 comma space y greater or equal than 0 space x plus y less or equal than 8... left parenthesis 1 right parenthesis x less or equal than 5 space space space space space.... left parenthesis 2 right parenthesis y less or equal than 5 space space space space space space... left parenthesis 3 right parenthesis x plus y greater or equal than 4.... left parenthesis 4 right parenthesis G r a p h space t h e space a b o v e space e q u a t i o n s space a s space f o l o w s colon Answered by Vimala Ramamurthy | 24 Oct, 2015, 02:02: PM

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CBSE 12-science - Maths
using graph, maximize z=4x+3y subject to the constraints x+y=9, 9x+2y=18
Asked by gargisha381 | 26 May, 2022, 12:24: PM
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CBSE 12-science - Maths
in ncert chapter 12 exercise 1 question no. 2 why we cant take points of x+2y=8 ... -24 should be the minimum value which comes from the point (8,0)..
Asked by ABHILASHA | 20 Apr, 2021, 12:07: PM
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CBSE 12-science - Maths
Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops D, E and F whose requirements are 60, 50 and 40 quintals respectively. The cost of transportation per quintals form the godowns to the shops are given in following table To/Form A B D E F 6 3 2.5 4 2 3 How would the supplies be transported in order that the transportation cost is minimum. What is the minimum cost?
Asked by Topperlearning User | 22 Sep, 2014, 10:45: AM
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CBSE 12-science - Maths
An oil company has two depots A and B with capacities 7000 and 4000 respectively. The company is to supply oil to three petrol pumps. D, E and F whose requirements are 4500 , 3000 and 3500 respectively. The distance (in km) between the depots and petrol pump is given as follows:   To/From A B DEF 763 342 How would the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?
Asked by Topperlearning User | 12 Sep, 2014, 03:47: PM
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CBSE 12-science - Maths
An aeroplane can carry a maximum of 200 passengers. A profit of Rs 400 is made on each first class ticket and a profit of Rs 300 is made on each economy class ticket. The airline reserves at least 20 seats for first class. However, at least 4 times as many passengers prefer to travel by economy class to by the first class. Determine how many each type of ticket must be sold in order to maximum the profit for the airline. What is maximum profit?
Asked by Topperlearning User | 31 Jul, 2016, 07:21: PM
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CBSE 12-science - Maths
A brick manufacturer has two depots, A and B, with stocks of 30,000 and 20.000 bricks respectively. He receives orders from three builders P, Q and R for 15,000, 20,000 and 15,000 bricks respectively. The cost in Rs of transporting 1000 bricks to the builders from the depots are given below :                  From To P Q R A 40 20 30 B 20 60 40           How should the manufacturer fulfil the orders so as to keep the cost of transportation minimum ? Formulate the above linear programming problem.
Asked by Topperlearning User | 31 Jul, 2016, 06:04: PM
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CBSE 12-science - Maths
An aeroplane can carry a maximum of 200 passengers. A profit of Rs. 1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket.  The airline reserves at least 20 seats for executive class.  However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline.  What is the maximum profit?
Asked by Topperlearning User | 31 Jul, 2016, 05:58: PM
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CBSE 12-science - Maths
There is a factory located at each of the two places  P and Q. From these location, a certain commodity is delivered to each of these depots situated at A, B and C. The weekly requirements of the depots are respectively 5, 5 and 4 units of the commodity while the production capacity of the factories at P and Q are respectively 8 and 6 units. The cost of transportation per unit is given below :   To From                                     Cost (in Rs) A B C P 16 10 15 Q 10 12 10   How many units should be transported from each factory to each depot in order that the transportation cost in minimum. Formulate the above LPP mathematically and the solve it.
Asked by Topperlearning User | 31 Jul, 2016, 05:47: PM
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CBSE 12-science - Maths
A toy company manufactures two types of dolls A and B. Resources indicate that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is atmost half of that for dolls of type A. Further the production level of dolls of type A can exceed three times the production of dolls of other type of atleast 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B. How many each should be produced weekly in order to maximize profit?
Asked by Topperlearning User | 31 Jul, 2016, 08:05: PM
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CBSE 12-science - Maths
A company manufactures two types of souveniers. Souvenier of type A requires 5 minutes each for cutting and 10 minutes each for assembling souvenier B requires 8 minutes each of cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenier. How many souvenier of each type should the company manufactures in order to maximize the profit.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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