**2.** 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 3.5 tons for a C-47 and 10 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 44 planes could be used per day. - Each C-47 required 4 crew members per flight and the crew requirement for the C-54 was 5. The total number of personnel available per day could not exceed 200. - The Americans only had 32 C-54's available. Find the number of C-47’s and C-54’s the Americans used to maximize their carrying capacity. a. **Define the variables. Be specific with descriptive words.** \( x = \) \( y = \) b. **Clearly state the constraints (all inequalities) related to the feasible region.** - \( \) - \( \) - \( \) c. **State the objective function.** ____________________________________ d. **Use the graphical method to solve: Graph the solution region, showing the intercepts used. Label axes, units, points and lines. Find and label all corner points.** *The grid for the graph is on the next page.* **Show all necessary work.** e. **Find the number of C-47’s and C-54’s the Americans used to maximize their carrying capacity.**