Chapter 8.6, Problem 20E

Use the two steps for solving a linear programming problem, given in the box on page 606, to solve the problems in Exercises 17-23.

On June 24.1948. the former Soviet Union blocked all land and water routes through East Germany to Berlin. A gigantic airlift was organized using American and British planes to bring food, clothing. and other supplies to the more than 2 million people in West Berlin. The cargo capacity was 30,1000 cubic feet for an American plane and 20.000cubic feet for a British plane To break the Soviet blockade, the Western Allies had to maximize cargo capacity but were subject to the following restrictions:

• No more than 44 planes could be used.

• The larger American planes required 16 personnel per flight, double that of the requirement for the British planes, The total number of personnel available could not exceed 512.

• The cost of an American fight was $9000 and the cost of a British flight was $5000. Total weekly costs could not exceed $300,000.

Find the number of American and British planes that were used to maximize cargo capacity