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?

Sample Solution