A travel agent has to fly 1,000 people and 35,000 kg of baggage from London to Paris. Two types of aircrafts are available: A which takes 100 people and 2,000 kg of baggage, or B which takes 60 people and 3,000 kg of baggage. He can use no more than 16 aircrafts altogether..
Answers
Given : A travel agent has to fly 1,000 people and 35,000 kg of baggage from London to Paris. Two types of aircrafts are available: A which takes 100 people and 2,000 kg of baggage, or B which takes 60 people and 3,000 kg of baggage. He can use no more than 16 aircrafts altogether..
To find : Minimum aircraft required
Solution:
100x + 60y ≥ 1000
=> 5x + 3y ≥ 50
2000x + 3000y ≥ 35000
=> 2x + 3y ≥ 35
x + y ≤ 16
x = 1 , y = 15 =>
x = 13 , y = 3
x = 5 , y = 25/3 is optimal solution but aircraft can not be in fraction
x = 5 , y = 9
x = 6 , y = 8
x = 4 , y = 10
x = 7 , y = 7
so minimum 14 aircrafts required
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