{"id":699,"date":"2016-10-19T03:30:00","date_gmt":"2016-10-19T03:30:00","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&p=699"},"modified":"2017-04-04T18:50:33","modified_gmt":"2017-04-04T18:50:33","slug":"why-it-matters-linear-and-absolute-value-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/chapter\/why-it-matters-linear-and-absolute-value-functions\/","title":{"raw":"Why It Matters: Linear and Absolute Value Functions","rendered":"Why It Matters: Linear and Absolute Value Functions"},"content":{"raw":"![\"A](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/17164717\/pexels-photo-30127-300x200.jpg\")
Why Use Linear and Absolute Value Functions?<\/h2>\r\nYou have a great idea for a small business. \u00a0You and a friend have developed a battery-powered bike. \u00a0It\u2019s perfect for getting around a college campus, or even to local stops in town. \u00a0You enjoy making the bikes, but would it be a worthwhile business\u2014one from which you can earn a profit?\r\n\r\nThe profit your business can earn depends on two main factors. \u00a0First, it depends on how much it costs you to make the bikes. \u00a0These costs include the parts you buy to make each bike as well as any rent and utilities you pay for the location where you make the bikes. \u00a0And it would include any salaries you pay people to help you.\r\n\r\n \r\n\r\nSecond, profit depends on revenue, which is the amount of money you take in by selling the bikes.\r\n
Profit = Revenue \u2013 Costs<\/p>\r\nBoth revenue and costs are linear functions. \u00a0They depend on the number of bikes you sell. You can then rewrite the profit equation as a function:\r\n
[latex]P\\left(x\\right)=R\\left(x\\right)-C\\left(x\\right)[\/latex]<\/p>\r\nwhere [latex]P(x)[\/latex] is profit, [latex]R(x)[\/latex] is revenue, and [latex]C(x)[\/latex] is cost and [latex]x[\/latex] equal the number of bikes produced and sold.\r\n\r\n \r\n\r\nYou and your business partner determine that your fixed costs, those you can\u2019t change such as the room you rent for the business, are $1,600 and your variable costs, those associated with each bike, are $200. \u00a0If you sell each bike for $600, the table shows your profits for different numbers of bikes.\r\n\r\n \r\n
\r\n
\r\n\r\n\r\n| Number of bikes<\/td>\r\n | Profit ($)<\/td>\r\n<\/tr>\r\n |
\r\n| 2<\/td>\r\n | \u2013800<\/td>\r\n<\/tr>\r\n |
\r\n| 5<\/td>\r\n | 400<\/td>\r\n<\/tr>\r\n |
\r\n| 10<\/td>\r\n | 2,400<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\nSo if you only sell 2 bikes, you actually lose money. \u00a0But if you sell 5 or more bikes, you earn a profit.\r\n\r\n \t- How can you figure out whether you will have a profit or a loss?<\/li>\r\n \t
- And how can you determine how many bikes you need to sell to break even?<\/li>\r\n \t
- How will shifting your price affect your profits?<\/li>\r\n<\/ul>\r\n \r\n\r\nIn this module you\u2019ll find out how to answer all of these questions. \u00a0Read on to learn how you might get your business up and running. \u00a0At the end of the module we\u2019ll revisit your bike business to find out the very point at which you\u2019ll start to earn a profit.\r\n\r\n \r\n
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