The cargo capacity is 30,000 cubic feet for Type A planes and 20,000 cubic feet for Type B planes. The cargo capacity is to be maximized subject to the following restrictions. 1) No more than 44 planes could be used. 2) The larger Type A planes required 14 personnel per flight, double that of the requirement for Type B planes. The total number of personnel available could not exceed 448. 3) The cost of flying Type A planes was $\$ 7000$ and the cost of flying Type B planes was $\$ 6000$. Total weekly costs could not exceed $\$ 284,000$. Find the number of Type A and Type B planes that were used to maximize cargo capacity. To maximize cargo capacity, $\square$ Type A and $\square$ Type $B$ planes were used.

Step 1 ：The problem is to maximize the cargo capacity of a fleet of planes, subject to certain constraints. The fleet consists of two types of planes: Type A and Type B. The cargo capacity is 30,000 cubic feet for Type A planes and 20,000 cubic feet for Type B planes.

Step 2 ：The constraints are as follows: No more than 44 planes could be used. The larger Type A planes required 14 personnel per flight, double that of the requirement for Type B planes. The total number of personnel available could not exceed 448. The cost of flying Type A planes was $7000 and the cost of flying Type B planes was $6000. Total weekly costs could not exceed $284,000.

Step 3 ：We can formulate this problem as a linear programming problem. The objective function to be maximized is the total cargo capacity, which is the sum of the cargo capacities of the Type A and Type B planes. The constraints are the limitations on the number of planes, personnel, and costs.

Step 4 ：By solving the linear programming problem, we find that the optimal solution is to use 20 Type A planes and 24 Type B planes. This will maximize the cargo capacity while satisfying all the constraints.

Step 5 ：Final Answer: To maximize cargo capacity, \( \boxed{20} \) Type A and \( \boxed{24} \) Type B planes were used.