
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

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)

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

Why do you have all the "minus" signs in your inequalities? And why are you setting the constraints are greater than the listed limits?

it's not a mminus sign just a dash

He has to fly exactly 1000 people and 35000kg bagage.
$\displaystyle 0 \leq x+y \leq 16 $
$\displaystyle 100x+60y1000=0 $
$\displaystyle 2000x+3000y35000=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 $\displaystyle 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 :)