1 / 12

Linear Functions and Applications

This lesson focuses on break even analysis using linear functions. It teaches business professionals how to determine the break even point where revenue equals costs, signifying the start of profit. The course covers essential concepts such as supply and demand, equilibrium price and quantity, and the relationship between price and quantity. It also examines costs of manufacturing, including fixed and variable costs, providing a comprehensive understanding of concepts crucial for financial decision-making in business.

boris-pickett
Télécharger la présentation

Linear Functions and Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Linear Functions and Applications Lesson 1.2

  2. A Break Even Calculator • Consider this web site which helps a business person know when they are breaking even (starting to make money) Note that the graph is a line. Quite often, break even analysis involves a linear function.

  3. Linear Function • A relationship f defined by for real numbers m and b is a linear function • The independent variable is x • The dependent variable is y

  4. Supply and Demand • Economists consider price to be the independent variable • However • They choose to plot price, p, on the vertical axis • Thus our text will consider p = f(q) That is price is a function of quantity • Graph the function(the calculator requiresthat x be used, not q)

  5. Supply and Demand • The demand for an item can also be represented by a linear function • On the same set of axes, graph Note: we are only interested in positive values, Quadrant 1. Reset the window with ♦E

  6. Supply and Demand • Set window for 0 < x < 3, 0 < y < 5 • Use the Trace feature (F3) to note values of quantity and price Supply Demand Price Quantity

  7. Supply and Demand • What is the price and quantity where the two functions are equal? • This is called the point of equilibrium Intersection may be found symbolically or by the calculator. Supply Demand Price Quantity

  8. Surplus Shortage Supply and Demand • Surplus is when excess supply exists • Shortage is when demand exceeds supply Supply Demand

  9. Cost Analysis • Cost of manufacturing an item usually consists of • Fixed cost (rent, utilities, etc.) • Cost per item (labor, materials, shipping …) • This fits the description of a linear function • The slope m is considered the "marginal cost" • The y-intercept b is the fixed cost

  10. Break Even Analysis • We compare Cost function with Revenue Function • Revenue is price times number sold • Usually you must sell a certain number of items to cover the fixed costs … beyond that you are making a profit • When R(x) > C(x) • The break even point is when R(x) = C(x)

  11. Profit C(x) loss R(x) Break Even Analysis • Given • Graph both and determine the point of equilibrium

  12. Assignment • Lesson 1.2 • Page 28 • Exercises 1 – 25 odd,29, 31, 37, 39

More Related