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?

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