Questions are in the attached documentation.

• Please submit your reports either in a Word or a PowerPoint file (only one format is enough). There is no page limit.
• Please submit your R codes for Parts I and II (the optimization of the promotional campaigns).

Part 1 Questions:

• Determine the decision variables
• Formulate the optimization model with all the constraints
• • Coding in R, find the optimal number of advertisements to run in each media that maximize the expected number of exposures while satisfying all the constraints. 
• o What is the optimal profit value? 
• o What are the optimal values for the variables? 

Part 2 Questions:

• Using your results from Part I, formulate the total profit (as defined by Vijay). 
• • Use R (or any other language) to determine the optimal number of ads to run in each medium to maximize the total profit while satisfying all the constraints in Part I. 
• o What is the optimal profit value? 
• o What are the optimal values for the variables? 
• o Based on your calculation, what can you conclude about the accuracy of Vjay’s approximation in Part I (i.e., finding the optimal variables by using the expected number of exposures)? 

Part 3 Questions:

• Formulate the profit function for Vijay’s ordering problem. 
• • What is the decision variable? 
• • Determine the optimal number of gallons of Amour du jour for which Amber must order raw materials each week to maximize the restaurant’s profit. What is the optimal profit?