# linear programming

• Jun 24th 2009, 03:11 PM
hi00000
linear programming
A travel agent has to fly 1000 people and 35000 kg of baggage from Hong Kong to Shanghai. Two type of aircraft are available:
"A" which takes 100 people and 2000 kg of baggage, or "B" which takes 60 people and 3000 baggage. he can use no more than 16 aircraft altogether. write dowm three inegualities which must be satisfied if he uses x of A and Y of B
• Jun 24th 2009, 04:02 PM
stapel
Write down the usual physical constraints, based on the fact that you can't have negative numbers of planes.

Create the "no more than sixteen planes" constraint.

Then create two more constraints based on the passengers and the weight of the baggage.

Please reply with what you create, and we can then go from there.

(Wink)
• Jun 24th 2009, 04:38 PM
hi00000
so is it - x+y<16
- 100x + 60y > 1000
- 2000x + 300y> 35000

i'm not that sure ....so can you tell me if it's right
• Jun 24th 2009, 05:14 PM
stapel
Why do you have all the "minus" signs in your inequalities? And why are you setting the constraints are greater than the listed limits?
• Jun 24th 2009, 11:42 PM
hi00000
it's not a mminus sign just a dash
• Jun 25th 2009, 12:13 AM
Twig
He has to fly exactly 1000 people and 35000kg bagage.

$0 \leq x+y \leq 16$

$100x+60y-1000=0$

$2000x+3000y-35000=0$

Now, I just made up some figures of the cost of using a plane.

Lets say using plane A costs 1 unit, and plane B 1.5 units.

So the cost function to minimize becomes $f(x,y)=x+1.5y$

I used MATLABS function linprog to solve this, this gave x = 5 , and y = 8.3333...

If you donīt know how to use the linprog function you can always ask :)