Business Calculus Project
Hello, please no plagiarism no ai, you don’t have to show your face, just record your voice and the paper that you are going to be solving the problems on, im gonna you use your video as an example and i am gonna recreate it showing my face and stuff,this is my last assignment for the semester make sure to do everything right thank you!
Project Objectives:
• Solve a business application problem related to definite integrals by setting up and evaluating definite integrals.
• Interpret (in-context) the graphical implication of a definite integral.
For this project you will create a video presentation. In the video presentation you will explain the concepts and mathematical processes involved in solving the given problems in the two tasks below:
Task #1
Purpose: Create a business example around two important business concepts, the consumer’s surplus and the producer’s surplus (CS and PS).
Watch the following math talk video if you haven’t done so already to get an idea about creating a business example related to CS and PS.
Video:
Think about a similar situation where consumer’s and producer’s surplus apply. In your video presentation first explain the meaning of consumer’s and producer’s surplus (using your own words, do not read from a script!) then, give an example of a similar situation (similar to what you saw in the math talk video above, but of course a different example). Please note that in Task 2 you will be asked to use your business example that you are giving in this task, so select your example wisely. You may want to read through Task 1 and Task 2 (look at the provided examples) before you think about your own business example.
Remember not to read from script, you are teaching your audience about a real-life application of consumer’s and producer’s surplus. Acquire the knowledge needed to explain these concepts by studying using the provided learning material then share your knowledge, share what you’ve learned!
Task #2
Purpose: Set up and solve definite integrals to find consumer’s and producer’s surplus and interpret the definite integrals graphically.
Before you start recording, take the following steps:
1. Refer to Task #1, your business example. In the steps below you are tasked to produce sample data for your business example and use the sample data to find two lines/curves and their equations, namely the demand curve and its equation and the supply curve and its equation.
2. Come up with some example numbers (figures) to use them as your sample data. If you are using an actual business example where data exists for your business example, use that data and identify the source where the data came from. If you are making up your sample data, consider the following: 1) As price of the goods decrease, more people can afford the product so the demand increases. This results in the demand function to be a decreasing curve (or a decreasing line). On the other hand, as the price goes up the producers will produce more to make more profit. This results in the supply function to be an increasing curve (or an increasing line). See the following student example for a made-up sample data: ” Let’s suppose that there is an incremental drop in the price of a new dishwasher. As the price drops, a larger number of consumers are able to afford the new dishwasher. The dropped prices and the number of dishwashers sold are as follows: {$400 (10 dishwashers sold at this price), $470 (6 dishwashers sold at this price), $500 (4 dishwashers sold at this price), $550 (3 dishwashers sold at this price), $600 (only 2 dishwashers sold at this price)}; Now let’s look at a producer that’s producing this dishwasher. The price the producer would be willing to charge along with the number of dishwashers produced are as follows:{$450 (5 dishwashers produced), $460 (6 dishwashers produced), $475 (10 dishwashers produced), $485 (12 dishwashers produced), $500 (15 dishwashers produced)}”
3. Next you need to find D(x)
, the demand function, and S(x)
, the supply function using your sample data. This requires data fitting to find the best equation that could model your situation. To do so, enter your sample data into an excel spreadsheet. You will need to do this twice (or using two different sets of columns), to find the equation for D(x) and next to find the equation for S(x). To find D(x) enter the consumer data into two columns (for the student example above, the student will enter {10, 6, 4, 3, 2} in the first column for quantity and{$400, $470, $500, $550, $600} in the second column for price, then based on your scatter plot choose the best fitting curve (add trendline). I suggest you assume a linear model for both the demand curve and the supply curve for simplicity of your calculations later when you are integrating. See the tutorial video below to learn how to find the best fitting curve and its equation. The tutorial shows a cubic curve fitting, based on your scatter plot you can choose linear or a degree two polynomial. Once again I suggest that you use a linear model which results in a linear equation.
4. Identify the point of equilibrium (x,p¯). This is the point of intersection of demand and supply equations. You would need to clearly explain in your video presentation how you found this point, what mathematical steps did you take to find the point of equilibrium. How do we find the point of intersection of two equations in general (the point(s) they have in common)?
5. Graph D(x)
and S(x)
on the same coordinate system where x-axis is the quantity and the y-axis is the price. Clearly show the point of equilibrium on your graph. Shade and clearly label the areas that represent consumer’s and producer’s surplus. (Desmos could be used to generate the graphs or graph by hand)
6. Set up and solve the integrals to compute consumer’s and producer’s surplus.
Video:
Now you are ready to record:
1. In your video presentation walk us through the steps and the process of finding the equations for consumer’s surplus, D(x)
and producer’s surplus, S(x)
. (To find these two equations, you would need to utilize your sample data and excel to find a best fitting model (line or curve) and use excel to find the curve’s or the line’s equation)
2. In your video presentation share the graphical representation of D(x)
and S(x)
. This includes the graphs of supply and demand curves (graphed on the same xy-plane).
3. Talk about the graphical implication of definite integrals. On your graph shade the area that indicates consumer’s surplus. On your graph shade the area that indicates producer’s surplus. What does a definite integral represent graphically? What is your understanding of a definite integral?
4. In your video presentation explain how to set up each definite integral. (one for consumer’s surplus and one for producer’s surplus) and how to select the limits of integration.
5. In your video presentation explain how to evaluate each definite integral step by step. Identify any methods used to evaluate the integral.
6. Finally in your video presentation tell us what do the results of these definite integrals say about your example product.
Video Presentation Requirements:
• Use ScreenPal or zoom to record your video presentation.
• Video presentation should not exceed 30 minutes.
• Introduce yourself in the beginning of the video presentation (I need to know who is presenting, I need to see your face (at least during the introduction))
• You are assessed on your knowledge of integration and the business application of definite integrals. Reading from script or showing a solved integral are not allowed. Your task is to teach your audience all the details and steps involved from setting up a definite integral to evaluating it.
• There will also be a heavy grading weight on graphical implication of CS and PS. Do you have a clear understanding of what a definite integral represents and are you able to describe it graphically.
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