3. Using the exact same problem, variables, objective function, and constraints in problem 2, solve using the Simplex Method. Show all your work, including row operations and matrices.

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 Americans had two types of planes available, the C-47 Skytrain and the C-54 Skymaster. The carrying capacity was 5.5 tons for a C-47 and 15 tons for a C-54. To break the Soviet blockade, the Western Allies had to maximize carrying capacity, but the Americans were limited by the following restrictions:

No more than 50 planes could be used per day.

Each C-47 required 4 crew members per flight and the crew requirement for the C-54 was 6. The total number of personnel available per day could not exceed 240.

The Americans only had 30 C-54s available.

Find the number of C-47s and C-54s the Americans used to maximize their carrying capacity.

a. Convert each constraint from problem 2 into an equation by adding slack variables and set up the initial simplex matrix.

b. Perform all pivots necessary using row operations to transform the matrix until the solution is feasible. 6 State the number of C-47s and C-54s the Americans used to maximize their carrying capacity.

c. What are the advantages/disadvantages of solving this liner programming problem using the graphing method vs. the simplex method? Justify your answer.