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Misc 7 - An oil company has two depots A and B with capacities

Misc 7 - Chapter 12 Class 12 Linear Programming - Part 2
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Misc 7 - Chapter 12 Class 12 Linear Programming - Part 4
Misc 7 - Chapter 12 Class 12 Linear Programming - Part 5
Misc 7 - Chapter 12 Class 12 Linear Programming - Part 6
Misc 7 - Chapter 12 Class 12 Linear Programming - Part 7
Misc 7 - Chapter 12 Class 12 Linear Programming - Part 8

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Misc 7 An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L, 3000L and 3500L respectively. The distances (in km) between the depots and the petrol pumps is given in the following table: Assuming that the transportation cost of 10 litres of oil is Re 1 per km, how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost? Let depot A transport x litres to petrol pump D depot A transport y litres to petrol pump E Transportation Cost for 10 litres = Rs 1 Transportation Cost for 1 litres = Rs 1/10 = Rs 0.1 Hence, Since number of litres transported to each depot must be greater than or equal to zero -: ∴ x ≥ 0, y ≥ 0 7000 − (x + y) ≥ 0 x + y ≤ 7000 4500 – x ≥ 0 x ≤ 4500 3000 − y ≥ 0 y ≤ 3000 x + y − 3500 ≥ 0 x + y ≥ 3500 As, we need to Minimize the cost of transportation, Hence the function used here is minimize Z. Total Transportation Cost : Z = 0.7x + 0.6y + 0.3 (7000 − (x + y)) + 0.3 (4500 − x) + 0.4(3000 – y) + 0.2 (x + y – 3500) Z = 0.3x + 0.1y + 3950 Hence, Minimize Z = 0.3x + 0.1y + 3950 Combing all constraints : Minimize Z = 0.3x + 0.1y + 3950 Subject to constraints : x + y ≤ 7000 y ≤ 3500 x ≤ 4500 x + y ≥ 3500 x, y ≥ 0 Hence, transportation cost will be Minimum if : Minimum Cost = Rs 4400 From A : 50, 3000, 3500 litres to petrol pump D, E, F respectively From B : 4000, 0, 0 litres to petrol pump D, E, F respectively

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.