1. ## another LP question

there are 3 electorates, A B C. Gov wants to distribute funds according to.

let x,y,x=number in millions that electorate A,B,C receive.

cost=x+y+z,

total should not exceed 48 million, A should receive no less then 10 million, B should receive at least 5million more then C, and C should receive at least the average received by A and B. Then minimize the cost of the gov payouts.

Minimize: c=x+y+z
subject to: x>=10
x+y+z<=48
y-5x>=0
z-x/2-y/2>=0
x,y,z>=0
I dont think this is right, and there is a mistake somewhere but cant find it.

2. First, state the problem:

We are going to minimize $c = x + y + z$ under the constraint that $x \geq 10$. So we get a system of equations:

$x + y + z \leq 48$ (Total Should Not Exceed 48 Million.)

$x - z \geq 5$ (B should receive at least 5 Million more than C, which means that their difference must be greater than or equal to 5 Million.)

$z \geq \frac{x + y}{2}$

$2z - x - y \geq 0$ (C should receive at least the average received by A and B. This means that x and y taken from 2 times z should be greater than or equal to 0.)

Try solving the problem with this set up. If you have anymore questions feel free to ask.