# Ideas and/or references for projects for a business calculus course

I have undertaken the teaching a business calculus course for this semester (spring II).
The various assesments for the students, include quizzes/hw/midterms/final exams, adjusted with suitable weights, and a project which counts for 10% of the total grade.
The project we have been using for the last couple of semesters revolves around break-even analysis and includes:

• designing and pricing a product,
• organizing a poll
• utilizing Excel to interpolate the data from the poll in order to construct the demand function,
• constructing cost-revenue-profit functions,
• optimizing the revenue and the profit,
• comparisons between the various otpimizations,
• critical questions on the procedures, ... etc

This semester (spring II) we have decided to update the various assesments, starting by redesigning the project for the course.

So my question is the following:

Are there some good ideas for projects suitable for a 1st year business calculus course?

Some remarks to be taken into account:

1. I am interested either in some references (papers/online etc) or in some explicit description of ideas.
2. The redesigned project will have an upgraded weight (smt like 15%-20% of the total grade).
3. One of the weaknesses i see (in the resources we have already been using) has to do with the fact that our current project actually stops at methods of differential calculus (1st/2nd derivative criteria for optimization, etc). Since our syllabus also includes integral calculus + multivariable calculus (partial derivatives+optimization of multivariable functions), i would like -ideally- some project which makes full use of the mathematical arsenal developed during the course.
4. it would be interesting if we could include some module related to to the law of supply/demand and the market equilibrium (instead of break-even analysis) or maybe combine both.
5. It would also be interesting and to a certain extend desirable -but not the main thing- if we could include the use of technology: for example utilizing a CAS like WolframAlpha would be really nice!
6. The course will be delivered online. It is the first time we are doing this (actually during Spring I, half of the course was delivered online, due to the well-known circumstances). I am not sure if this affects my question (i leave it to the potential answerers to judge), but it is not the main point of the question.
7. FWIW, the main textbook we are using right now is Applied Calculus, Hoffmann/Bradley/Sobecki/Price, 11th edition

So, i am open to interesting ideas and/or references.
Thank you in advance!

• I also teach business calculus at FIU almost every semester and your original project sounds very interesting. Would you be open to sharing it, given proper credit of course? A fellow professor
– KJG
Commented Aug 4, 2021 at 13:47
• @KJG Another good way to do this would be to say what you said as a new question on the site, and then link KonKan to the question Commented Aug 4, 2021 at 15:01
• @KJG, thank you for your interest. We have already updated the project by adding one more module (utilizing applications of integral calculus). I find your suggestion very interesting, however, since other profs before me have contributed to the development of the project, i have to ask for their consensus and i will discuss this with the head of our department as well. In any case, i will let you know asap! Commented Aug 8, 2021 at 19:20
• @KJG after discussing this with colleagues and having their consensus i' d love to tell you that everybody agrees on sharing the project with you. I suggest we contact through emails. My address is [email protected] Commented Sep 6, 2021 at 21:03

## 1 Answer

"So, i am open to interesting ideas and/or references."

More in the idea realm than the "everything you asked for", but take a look at petroleum economics. Especially useful if you are in a petroleum producing country.

Ref1: http://investors.clr.com/presentations (open the MAR2018 presentation): pages 15 and 17 show a simple optimization problem.

You can also make a simple single well economics model and do various optimizations with that. These are your familiar break even calculations. For instance the trade-off of a fancier well completion versus accelerating or increasing the EUR. The one nice feature is that it's not just increasing revenue. The acceleration impact also can be very important in improving NPV. Shale well models are actually done with months, not just with the year convention of most NPV models.

Personally, I would just build the well NPV model yourself (simpler). But if you want some references (some overly detailed), see here: https://www.google.com/search?q=oil+well+NPV+model+excel&hl=en&sxsrf=ALeKk03E2qKbEjB_q-5qZ_tTpxPMjsOtuA:1588029457546&source=lnms&tbm=vid&sa=X&ved=2ahUKEwixxtbd3onpAhUHg3IEHddiCbAQ_AUoAnoECAsQBA&biw=1920&bih=966

I'm really not a fan of CAS and worry that you're combining too much here (weaker students, basic calculus concepts, a project, and business insights...and then ALSO CAS). But if you must needs involve it, some of the more complicated decline curves in modified Arps models, are probably fun to play with with CAS. Also, you're doing integration when looking at EUR. And that's a concept you wanted to bring into the course.

https://www.youtube.com/watch?v=blvorGxNtxM is a decent overview. But there are a lot of other articles and videos out there that give you an overview of this topic.

• Thank you for your answer. It seems to integrate interesting ideas and concepts. However, i have to tell you i have very limited understanding of economics myself and i can barely understand terms like ""EUR", "NPV models" and "Arps models" but i am experienced in modeling. I am a physicist and a mathematician at heart! So i will try to study your references and the models you cite. Your contribution is valuable! Commented Apr 27, 2020 at 23:46
• EUR is the estimated ultimate recovery. Total volume of oil that comes out of an oil well. The area under the curve of production rate over time. I.e. an integral. The simplest model is exponential decay, which as you know is a finite integral. Other models seem to fit the data well at times (hyperbolic). These may be nonfinite but in practice this is dealt with by assuming a transition to exponential late in life or a set rate (or age) when the well is stopped for economic reasons. See here: petrowiki.org/Production_forecasting_decline_curve_analysis Commented Apr 28, 2020 at 1:43
• Skip the NPV modeling. Sad to say lots of business students don't understand them (or the microeconomic insights from them either). What would be crushingly simple math to a physicist is a turnoff to all except the most Excel loving finance types within the business school. youtube.com/watch?v=HFFkFMfotT0 Commented Apr 28, 2020 at 1:48