Lab 4: Section 7.5-7.5 Simplex Method with Applications Math 1324 Instructions: Show all work and write your solutions to the problem neatly on this worksheet. Draw a box around your final answer. If you need help, feel free to consult with me during office hours or go to the math lab and ask for assistance. This first problem should look familiar, it was on Lab 3. We are now going to solve it using Simplex instead of graphing. 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. 1. Set up your word problem. If you completed this problem correctly on Lab 3, you should copy the answers to problem 6-8 here Define the variables. Be specific with descriptive words. Clearly state the constraints (all inequalities) related to the feasible region. State the objective function. 2. Convert the constraints and the objective functions into appropriate equations for the Simple Method using slack variables where appropriate 3. Write the initial simplex matrix 4. Circle the first pivot point on the matrix in the previous problem, then write a list of all tow operations necessary to perform the first pivot $. After completing the first pivot, is your matrix in its final simplex form? If not, state the next pivot point and all row operations necessary to perform the pivot. 6. Write your final simplex tableau. Lab 4: Section 74-7.5 Page 2 7. Which variables are BASIC variables! 8. Which variables are NON-BASIC variables? 9. State the number of C-47's and C-54's the Americans used to maximize their carrying capacity. 10. Did you get the same answer on this problem as you did using the graphical method on Lab 3? If not use at least one complete sentence to explain why your answers are different An investor is considering three types of investments: a high-risk venture into oil leases with a potential return of 15%, a medium-risk investment in bonds with a 9% retum, and a relatively safe stock investment with a 5% retum. He has $50,000 to invest. Because of the risk, he will limit his investment in oil leases and bonds to 30% and his investment in oil leases and stock to 50%. How much should he invest in cach to maximize his return, assuming investment returns are as expected? 11. Define the variables. Be specific with descriptive words. - 12. Clearly state the constraints (all inequalities) related to the feasible region. 13. State the objective function, Lab 4: Section 74-75 Page 3