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Business Applications of Calculus
Transcript of Business Applications of Calculus
Business Applications of Calculus
A Closer Look at...
How calculus can be applied in the business field!
Professor Joy D'Andrea
Heather, Tim, Amy, Pete, & Lauren
Applications With Heather
"Some schools may require more advanced topics such as linear programming or calculus for accounting majors. However you will never, ever, need this kind of more advanced math in accounting. The courses are really just used as screening devices and to add status to a program. You just have to put up with them or find a different program.” -Greg Mostyn, Mission College
Applications With Tim
Reliable Measurement System
Helps Business Managers to maximize profits
Problem Solving Skills
Applications with Lauren
Mandatory course for Economic, Business, and Accounting Majors
Interest on loans, marginal revenue/cost
Used in careers of Statisticians, Economists, Accountants, and Business Owners
Derivatives to achieve optimization
Applications with Pete
With a background of 12 years in professional sales, marketing, and distribution, where Pete has worked in a variety of positions and roles in businesses, he still has yet to use Business Calculus; however, statistics has often come to his aid.
After some research, he has found that calculus is helpful in many of the applied sciences but less in the field of general business.
Pete hopes that upon the completion of this class he will have found ways to incorporate business calculus into his work so that they can be more successful, increase profitability, and make better decisions.
Applications with Amy
Calculus is useful in Business because:
1. It helps you to practice and develop your logic/reasoning skills.
2. An operations research analyst will use calculus when observing different processes at a manufacturing corporation. By considering the value of different variables, they can help a company improve operating efficiency, increase production, and raise profits.
3. Differential Calculus helps in solving problems of finding maximum profit or minimum cost.
4. The market and all business runs on a time scale that can most accurately be predicted by calculus instead of spread sheets, which rely on intervals of time.
Calculus provides an accurate and measurable way to record changes in variables using numbers and mathematics.
Calculus is used by economists when they are looking to determine the most opportune time to buy or sell good or when considering the affects of price on how much consumers purchase.
Calculus helps to broaden one's perspective of how to solve problems in life.
A word from Tim:
"Calculus is so dang hard that everything in life seems simple by comparison."
Marginal Revenue Problem
Derivatives in calculus can be used to determine maximum profit, minimum cost, rate of change of cost, and how to maximize/minimize
Functions are used to illustrate the relationship between 2 or more variables.
Derivatives are used to show the rate of change of variables in response to other variables.
Calculus can be used to figure out how much interest is paid on a loan.
In economics calculus can be used when working on concepts like finding the margins.
While the applications of calculus in business may not be obvious right away, Calculus can be very beneficial when working on...
Problem Solving Skills, and Economic Concepts.
Obtaining a degree in business, economics, and accounting,
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Locate the cost and revenue functions. When solving the maximize profit in calculus, the problem will generally provide you with the cost and revenue function to start off, but will ask you to solve for "x." In a maximize profit problem, the "x" represents the number of units you must produce to generate the most profit.
Plug your cost and revenue functions into the maximize profit equation: P(x) = R(x) - C(x) where "R(x)" is the revenue function and "C(x)" is the cost function. For example, if your cost function is C(x) = -15x + 10 and your revenue function is R(x) = .10x^2 + 2x, then your equation would be:
P(x) = (.10x^2 + 2x) - (-15x + 10)
Simplify the maximize profit equation you found in Step 2. For example, if you take the equation P(x) = (.10x^2 + 2x) - (-15x + 10) and simplified it, it would look like this:
P(x) = .10x^2 - 17x - 10
Take the derivative of the simplified equation and set it to zero in order to solve for "x." For example, if our equation was P(x) = .10x^2 - 17x - 10, the derivative set to zero would be:
0 = .20x - 17
Find the number of units you will have to produce to maximize the profit by solving for "x." For example, if the derivative of our equation is 0 = .20x - 17, you would need to produce 85 units to create a maximum profit.