Help finding linear inequalities and constraints for objective function (word problem)

Question

I am working on a homework problem, and I an stuck on trying to get the inequalities and constraints needed for set-up to solve and graph it. If anyone could help, I would very much appreciate it. Thanks ahead of time!

Problem:

The American and British governments want to supply aid to the people in an impoverished nation. An airlift will be organized to provide food, clothing, and other supplies. The cargo capacity for an American Plane is 30000 cubic feet and is 20000 cubic feet for a British plane. The airlift will be limited by the following conditions:

No more than 48 planes can be used.

The larger American planes require 12 personnel per flight, double that of the requirement for British planes. The number of personnel available is 444.

Find the number of American and British planes that should be used to maximize cargo capacity.

What is the maximum cargo capacity?

Answer 1

Let x be the number of American planes and y be the number of British planes. Let C be the amount of total cargo. The objective function is:

C = 30,000x + 20,000y

Constraints:

1. No more than 48 planes can be used: x + y ≤ 48
2. The larger American planes require 12 personnel per flight, double that of the requirement for British planes. The number of personnel available is 444.: 12x + 6y ≤ 444
3. Since you can't have a negative number of planes, you also want x ≥ 0 and y ≥ 0

Can you finish it from here?