Elementary Calculus Midterm
Report Activity brief
BCO116 Elementary Calculus Online campus
Professor: Paulo Azevedo | [email protected]
Description Written report describing the various steps of the required calculations. The questions are shown below.
Format Written report:
? DOC, DOCX or PDF file ? No specific formatting or styling rules. ? No need for references.
You may paste scanned images or photographs from your handwritten work a few sentences may have to be typed for the submission to be accepted.
Goal(s) Test the students understanding of the Elementary Calculus topics covered from Week 1 to Week 4, namely functions, solving equations, graphing simple functions and differentiation.
Due date Date: Monday, June 21, 2021 Time: 14:00 CEST
Weight towards final grade
This activity has a weight of 40% towards the final grade.
Learning outcomes
1. Understand what a function is and interpret its applications in business
2. Recognize, classify and compare functions represented in a variety of ways, including graphical, numerical, analytical, or verbal in the business world
3. Describe the limits of functions from their graphs and/ or formulas.
4. Interpret the derivatives of functions
5. Describe the notions of continuity and differentiability to algebraic functions.
Assessment criteria
See the rubric below.
? Question 1 – 10%;
? Question 2 – 10%;
? Question 3 – 10%;
? Question 4 – 10%;
? Question 5 – 30%;
? Question 6 – 10%;
? Question 7 – 10%;
? Question 8 10%;
Questions
Company ABC produces and sells X electric pressure cookers per year. The price of the cookers is represented by P, in / unit. The relationship between
price and demand is given by: P=200?0.004 X.
1. Write the revenues function. (10%)
2. How many units should be produced, and at which price should the pressure cookers be sold, to maximize revenues? (10%)
Company ABC operates with fixed costs of 800 thousand euros (800 000 ) per year and variable costs of 40 per cooker.
3. Write the companys profit function. (10%)
4. How many units should be produced, and at which price should the pressure cookers be sold, to maximize the profit? (10%)
5. Draw a graph representing the above-mentioned situation (profit maximization). (30%)
The government decides to introduce a new tax on electric appliances of 10 per product. Taking this additional cost into account:
6. Write the companys new cost function. (10%)
7. Write the companys new profit function. (10%)
8. How many units should be produced, and at which price should the pressure cookers be sold, to maximize the profit under the new conditions? (10%)
Rubric
Task Between 90% and 100% Between 80% and 90% Between 60% and 80% Between 30% and 60% Between 0% and 30%
Calculation Result and process are correct, and answer is well explained (process is detailed).
Minor details may cause deduction of points.
Minor errors leading to wrong result, but explanation is clear and process is generally correct.
Some important errors revealing some confusion, but partially correct process.
Seemingly correct process and correct result, but no adequate explanation is provided
Important errors revealing significant misunderstanding of relevant concepts, but the process is not entirely wrong.
Wrong result, lacking any coherent explanation.
Graph Correct, readable and well presented, properly titled and labeled (including axes, and units if needed)
Some minor readability or presentation.
Important incorrections, but graphs still conveys most relevant information.
Serious incorrections rendering the graph almost useless, but correct type of graph and variables are used.
No graphs is presented, or graph completely misses the point (incorrect graph type and/ or variables)
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