GeekOfMath
New member
- Joined
- May 9, 2017
- Messages
- 6
Hello!
I need help with a couple of optimization problems that I'm unsure of how to begin. Any advice or help is welcome and much appreciated.
Question 1:
Collect data on several cans with the same mass of product but different sizes and collate the information in a table (already have)
A) Which can is the most economical? - i.e. the lowest ration of volume to surface area
B) What are the optimal dimensions of a can of this volume?
So I am a little confused on how to start answering these questions. It would be excellent if someone could me a pointer on where to start. I get the feeling A needs to a function relating surface area to volume ratio and then differentiated and then equaled to 0 to get the minimum value but still unsure of how to go about doing this. Thanks in advance!
I need help with a couple of optimization problems that I'm unsure of how to begin. Any advice or help is welcome and much appreciated.
Question 1:
Collect data on several cans with the same mass of product but different sizes and collate the information in a table (already have)
Product Name | Can 1 | Can 2 |
Printed volume | 300g | 300g |
Can Dimensions Height Diameter | Height – Approx 8cm Diameter – Approx 6.9cm | Height – Approx 10.1cm Diameter – Approx 6.1cm |
Actual volume of each can | V = πr2h = π x (6.9/2)2 x 8 = π x 3.452 x 8 = π x 11.9 x 8 = 299.08cm3 | V = πr2h = π x (6.1/2)2 x 10.1 = π x 3.052 x 10.1 = π x 9.3 x 10.1 = 295.09cm3 |
The surface area of each can | A = 2πrh + 2πr2 = 2π (6.9/2) x 8 + 2π x (6.9/2)2 = 2π x 3.45 x 8 + 2π x 3.452 = 248.2cm2 | A = 2πrh + 2πr2 = 2π (6.1/2) x 10.1 + 2π (6.1/2)2 = 2π x 3.05 x 10.1 + 2π x 3.052 = 252cm2 |
A) Which can is the most economical? - i.e. the lowest ration of volume to surface area
B) What are the optimal dimensions of a can of this volume?
So I am a little confused on how to start answering these questions. It would be excellent if someone could me a pointer on where to start. I get the feeling A needs to a function relating surface area to volume ratio and then differentiated and then equaled to 0 to get the minimum value but still unsure of how to go about doing this. Thanks in advance!