Construct a mathematical model to rank cafes. Remark: You may replace cafes with another service that you are more relatable to. (a) Build your first model. State the precise problem statement and all of your assumptions and variables. (b) Apply your first model to some cafes you have visited (best to include the bad and mediocre ones and your favorites). Assess the model outputs. (c) Discuss how you may improve the first model based on the results in (b). Propose your final model.

Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.

MANUAL SOLUTIONS DONT USE EXCEL

Atlantic hurricanes form off the western coast of Africa. As warm moist air rises, it begins to rotate around a low- pressure system. This rotation is sustained by warm ocean temperatures and a central low pressure. Once a sustained wind speed of 74 miles per hour is reached, the storm is considered a hurricane. As man-made climate change continues to increase the temperature of the Earth's oceans, it is expected that the strength of hurricanes will Typically, a lower central pressure within a hurricane's eye is associated with a higher wind speed. Here, statistical software (R/RStudio) will be used to explore this relationship by applying linear regression methods. Using a database of landfalling hurricanes in the United States, a linear regression will be used to correlate the central pressure of each hurricane to its maximum sustained wind speed. increase. Regression Plot y=942.196-0.884*x R^2=0.768 ----- ----------- -. •... •. 980 1000 940 960 900 920 Independent Variable (x)…