# Linear Programming Problem

Homework Statement:
A famine relief effort is being mounted and there are three types of food bundles that can be flown out during each delivery. Bundle 1 has 4 kg. of flour, 4 kg. of sugar and 12 litres of water. Bundle 2 has 12 kg. of flour, 4 kg. of sugar and 4 litres of water and Bundle 3 has 8 kg. of flour, 8 kg. of sugar and 8 litres of water. The relief agency has 5200 kg. of flour, 3800 kg. of sugar and 6000 litres of water for each shipment. Bundle 1 can provide for 10 people between deliveries, Bundle 2 for 8 people and Bundle 3 for 11 people. How many bundles of each type should the relief agency send on each flight in order to maximize the number of people being fed.
Do this problem by setting up a linear programming problem and determining the vertices of the feasibility set.
List the number of bundles of types 1, 2, and 3, separated with commas.
Relevant Equations:
Linear Programming
I am comfortable solving these types of problems, however I am having trouble setting up this problem and am unsure if I am doing this correctly so would someone be able to assist me?

I first wrote an equation for the people: 10x +8y +11z.

Then I made an equation for the flour: 4x + 12y + 8z <= 5200.
My equation for the sugar: 4x + 4y + 8z <= 3800.
My equation for the water: 12x + 4y + 8z <= 6000.
And then x>=0, y>=0, and z>=0.

Am I on the right track with this set up?

Thanks.