In this project, students were tasked with figuring out the optimal amount of ads to be purchased by a business. The business wants to buy both TV and radio ads to expand the amount of people reached by their advertisements. Students are given the cost of each ad and an overall budget. The amount of listeners and watchers of the ads are also given, providing enough information for the problem to be solved effectively.
To solve this project, student must exercise mathematical techniques such as:
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Does this project show how math can be applied to the real world? |
Yes it does! Everyday advertisers want to show off their product in an effective manner that will reach the most people for the lowest price. Any self respecting marketing team needs to understand how to optimize their budget to get the best results.
More ads seen = Greater possibility of product being sold Greater possibility of product being sold = More money More money = Better quality ads/more ads produced and seen |
What other careers could be interested in this type of analysis, aside from business?
Charities use this formula all the time. Health, International, Animal, and Education based charities are a few examples.
All share a common goal of sharing their message to receive funding. To effectively share their message, they need to plan out how many commercials they can produce within a certain budget. Charities use most of their funding towards the causes they stand for, so their marketing team needs to know how to budget. |
Other applications of linear programming in the real world
Farmers use linear programming to analyse and properly distribute their available land for crops. Certain crops cost more to plant, so the farmer would want to get the most out of his available land to plant more expensive crops. Finding out the max and min of how many seeds he can plant determines the harvest and how much income he will make that season.
Factories also use this to find out how many toys they will be able to produce within their budget. One toy may by $2 to produce while another is $5. The $2 toy takes longer to produce than the $5 toy. The factory then has to find out how much product they can make in a certain amount of hours available.
If you were the business owner in this lab and the manager brought you the results of the lab, why would it be important for the manager to be clear about the process and be able justify her conclusion? |
If the manager is unable to show her work and process of getting the results, that could mean an error may have occurred along the way. Any error could be a major liability to the company, costing us thousands of dollars for a misplaced decimal point.
By being able to explain her reasoning, that provides some security for the company to invest in this plan. Being a theoretical solution, showing only how many advertisements could possibly be seen, it's still a risk for the company. Having a thoroughly thought out plan is a more cost smart situation than not having one. |
Did this assignment change how you thought about the usefulness of math?
This project did, in fact, change how I looked at the usefulness of math in everyday life. Having to solve a project like this really put my math skills to the test. I used to think that I would just need to know addition, multiplication, addition, and subtraction when I left school and entered the work force. However, once we received this assignment I knew I was going to have to change my ideas real fast.
I like that way one of my math tutors explained Algebra to me. 'It's like the spicy version of PEMDAS." One he said that to me, it really started coming together. I was overthinking the math just because their were more variables and steps. Once I realized that it's all pretty much the same in application, solving this project became significantly easier. Algebra may not be my strongest subject, but I can know confidently say that I understand how to apply it to everyday life. |