Formulate the linear programming model for the issue algebraically. Group this in three sections: 1) Definition of Decision Variables, 2) Objective Function Equation, 3) Constraints Equations

Richelieu Specialty Paints Richelieu Specialty Paints is a company run by Amanda Richelieu. She is an artist and earned a BA degree with a major in Art and Design. The company was founded by Amanda's father and he recently asked her to take over managing it so that he could retire. Amanda agreed and left her interior design job with an architecture firm to assume the role. She is keen to develop the business further. The company makes a wide variety of paints, mostly targeted at fine artists. However, since Amanda has had experience in interior design she has determined that the company could apply its skills to develop new products for that industry and others. She knows that she hasn't yet developed her quantitative analysis skills to the point they need to be to run a company, so she is seeking assistance with four decisions that she needs to make. She would like to have a report from you providing recommendations for each decision, along with the background calculations that support your decisions. Decision 1: Marketing - Advertising Placement Amanda has a yearly advertising and promotions budget of $50,000. Her goal is to maximize the reach (the number of customers that see her company's ads or other marketing efforts). She is considering a mix of placing ads on art websites and in printed art magazines, as well as using targeted social media ad placements and appearances at art tradeshows. She wants to make sure that the company has an online presence, so would like to see at least 100 ads placed in any combination of websites and social media per year. However, she has data that suggests that if she advertises on the websites more than 60 times per year she will be wasting money. There are seven art tradeshows that the company could attend, but Amanda feels it is mandatory to attend at least the two most popular tradeshows. There are three major art magazines, each published monthly, that Amanda would like to advertise in. She could advertise in each of these once per month but would be comfortable reducing the frequency to a minimum of once every three months in each magazine and rotating the placements between the magazines. The reach and cost of each type of ad placement or event is shown below: Art Websites Social Art Media Tradeshows Print Magazine Ads Reach (number of people) 14000 12,000 5,000 10,000 Cost (dollars) 200 250 1,000 400 Recommend the appropriate mix of advertising and promotions for the company. Also comment on what would change if Amanda doubled her advertising and promotions budget. Estimate the increased reach