Report 2: A Technical Report: Write a report explaining the work that you did and what you learned. Assume that the reader is an "A" Calculus student at some other school. You need to explain minor details of the calculations. Your reader does not know the meanings of some terms, so these must be explained. You must also explain your general procedures. Your report should be completely independent of the project instructions. It should have an introduction that briefly states the purpose of the work and the key results, followed by a body that is organized into sections for easy readability. Keep in mind that you are writing about the problem, not your experience of solving it. ("The result is." rather than "First I looked at." and "I found that the result was."). The mathematics must be correct and well explained and the report must be readable and easy to study. For a complete analysis of the problem you will need to include the following: 1. A revenue function, R(q), for selling q bushels at a price p(q) 2. A total cost function, C(q), for buying a bushels 3. A total profit function, P(q), for buying and selling q bushels 4. A graph of the three functions on the same coordinate system. (label your axes) What price per bushel should she sell the beans to maximize her total profit? How many bushels would she need to sell? What price per bushel? 5. A graph of the derivative functions R' (q), C(q), and P'q) on the same coordinate system. (label your axes). Do the graphs of R' (q) and C(q) intersect? If so, describe the significance of the point of intersection. Does the graph of P' (q) intersect the q axis? If so, describe the significance of the point of intersection. 6. Compute the marginal profit for q = 1800. Describe what this means. 7. If the supplier raises the price of beans to BD 3.50 per bushel how many bushels should she buy to maximize the total profit? 8. The supplier changes the price so often that Ms. decides to find a formula that will tell her what quantity, q, to buy at k Bahraini Dinars per bushel. Find this formula that will maximize her total profits. Report 2: A Technical Report: Write a report explaining the work that you did and what you learned. Assume that the reader is an "A" Calculus student at some other school. You need to explain minor details of the calculations. Your reader does not know the meanings of some terms, so these must be explained. You must also explain your general procedures. Your report should be completely independent of the project instructions. It should have an introduction that briefly states the purpose of the work and the key results, followed by a body that is organized into sections for easy readability. Keep in mind that you are writing about the problem, not your experience of solving it. ("The result is." rather than "First I looked at." and "I found that the result was."). The mathematics must be correct and well explained and the report must be readable and easy to study. For a complete analysis of the problem you will need to include the following: 1. A revenue function, R(q), for selling q bushels at a price p(q) 2. A total cost function, C(q), for buying a bushels 3. A total profit function, P(q), for buying and selling q bushels 4. A graph of the three functions on the same coordinate system. (label your axes) What price per bushel should she sell the beans to maximize her total profit? How many bushels would she need to sell? What price per bushel? 5. A graph of the derivative functions R' (q), C(q), and P'q) on the same coordinate system. (label your axes). Do the graphs of R' (q) and C(q) intersect? If so, describe the significance of the point of intersection. Does the graph of P' (q) intersect the q axis? If so, describe the significance of the point of intersection. 6. Compute the marginal profit for q = 1800. Describe what this means. 7. If the supplier raises the price of beans to BD 3.50 per bushel how many bushels should she buy to maximize the total profit? 8. The supplier changes the price so often that Ms. decides to find a formula that will tell her what quantity, q, to buy at k Bahraini Dinars per bushel. Find this formula that will maximize her total profits
