Can Problem: 20 points AP Calculus AB/BC Name Period Date You are a production e

Question

Can Problem: 20 points AP Calculus AB/BC Name Period Date You are a production engine fora large food processing firm. Oae of your tasks is to analyze the packagin of materials and the least cost in their containers. Your task is to seleet a container with a specifie material and minimum cost and to provide a written report of your findings to the company president with your recommendations. g containers and determine whether the company is making the most efficient use d volume and determine whether it is constructed with the minimum amount of Your report should include the following information about the container. Measurements should be taken in centimeters. Final answers should be rounded to 3 decimal places volume. (1 pt) 1. Determine the altitude and radius of the original can and calculate the 2. Write the equation to be minimized. pt) 3. Provide a DETAILED algebraic solution with the dimensions for the minimum amount of material needed to construct the can. (2 pts.) Justify your answer. (I pt.) 4. Provide a graphical sketch of the minimum (1 pt.) (1 pt); surface area of the Calculate each of the following: surface area of the original can minimized can (I pt.); if 20000000 minimized can. (I pt) 5. cans are produced each year, find the total material saved with 6. If the metal costs $5 per square meter, calculate the monetary savings. (1 pt.) 7. The company also produces a 2nd type of can constructed from two different types of metal with the top and bottom costing S7 per square meter and the side costing $5 per square meter. Write an equation to minimize the cost of this can. ( pt.) 8. Provide a DETAILED algebraie solution with the dimensions for the can with minimum cost.(2 pts.) Justify your answer. (1 pt.) 9. Provide a graphical sketch of the minimum. l pt) nal can (1 pt.); cost of the new (I pt.) (Keep 6 decimals for the 10. Calculate each of the following using the two metals: cost of the origi savings for the 20000000 cans. can (1 pt.); and the total monetary s cost of the cans) Write a recommendation letter to the president for each of the 2 situations investigated. It should be typed and less than one pag investigated, but also any other related costs, aesthetics, practicality, etc. Just stating your findings will not get you full points. (3 pts.) 11. e. You should not only consider the financial aspect that you Radius- 5 cm Altitude-6 cm Problems-11 please

Explanation / Answer

4. In this question, you have to plot the equation to be minimized and show graphically the point of minima.

5. In this, you have to find the surface area of the can with initially given dimensions and then after obtaining new dimensions by minimizing the equation in the previous question. Then subtract to obtain the material saved for one can.

6. multiply $5 with material saved for 20000000 cans, obtained in last question.

7. Now since we have two different types of materials for sides and top bottom, so surface area eq. will be different and thus you have to minimize a different equation.

8. now you have to solve the minimization problem for equation obtained in the previous question.

9. Again just like the 4th question you have to plot the equation to be minimized and show graphically the point of minima.

10. Again you have to find total savings for this new can.

11. Now you have to write an entire summary of your research from 1st question to 10th question, like what you observed.

If you still have some doubt, feel free to comment and I will respond to your queries.

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