15.5 Exercises: Integer Optimization

Q1

John is interested in buying ads to market his new startup. He sees the following options:

Ad	Cost per ad	Reach	Limits
Radio Ad	$100	500	40
Newspaper Ad	$250	2000	10
Social Media Ad	$50	300	80

The “limits” in the table above are imposed by each advertiser, so the Newspaper will only run a maximum of 10 Newspaper Ads. Reach is an estimated number of people that the ad will reach, per ad that John buys (e.g. if he buys 1 Radio ad, it will reach 500 people. If he buys 2, it will reach 1000 people.)

Q1a) Identify the decision variables, objective function and constraints. Write out the optimization problem in a table.

Q1b) Write R code to solve this problem. What is the optimal solution, and what is the value of the objective function that this optimal solution?