The cargo capacity is 25,000 ft.³ for type a planes and 15,000 ft.³ for type B planes. The cargo capacity is to be maximized subject to the following restrictions. 1) no more than 62 planes could be used. 2) The larger type a planes required 18 personal per flight, double that of the requirement for type B planes. The total number of personnel available could not exceed 828. 3) The cost of flying type a plains was $8000 and the cost of flying type B plains was $5000. Total weekly costs could not exceed $400,000. Find the number of type a and type B planes that were used to maximize cargo capacity.