Cutlery Corner sells specialty knives to knife enthusiasts. They have a generous advertising budget to spread among four media channels: their recurring TV show, newspaper ads, radio spots, and social media. Tom, the owner and star of the TV show is adamant that the show air at least twice a day, seven days a week but decides you can allocate the rest of the budget as you see fit. The TV shows draws 20,000 interested viewers per airing and costs $2,000 per episode. Daily newspaper ads cost $1500 and can be run up to seven days a week. Given the level of readership for newspapers, you settle on a figure of 10,000 people reached per ad. Radio spots come in 15 second and 30 second durations 15 second spots in drive time cost $500 per airing and 30 second spots any other time of the day are a relative bargain at $250. Drive time spots are available twice a day (morning and evening commute) five days a week and reach 12,000, and the "any other time" spots could air up to six times a day seven days a week and reach 5,000 listeners per airing. The social media campaign is run out of a specialist's office and a burst of blogging, tweeting, vining and whatever else happens to be in fashion at the time costs $700 and reaches 10,000. Budget sis assumed to be $45,0000.

Naturally, it occurs to you that this could be modeled as a linear program, so you define your variables as: T = dollars spent on a TV campaign N = dollars spent on newspaper advertisements RF = dollars spent on fifteen second drive time radio advertisements

RT = dollars spent on thirty second radio advertisements S = dollars spent on the social media campaign

What is the objective function and constraints if the problem is set up to determine the way to reach the most potential customers? Setup the model, including the objective function and all constraints.