Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Problem: Cost Minimization of a Cylinder Can**
A cylindrical can needs to be constructed to hold 250 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can needs to be thicker, costing 0.06 cents per square centimeter. Find the dimensions for the can that will minimize the production cost.
**Helpful Information:**
- \( h \): height of the can
- \( r \): radius of the can
**Formulas:**
1. **Volume of a Cylinder:**
\[
V = \pi r^2 h
\]
2. **Area of the Sides:**
\[
A = 2 \pi r h
\]
3. **Area of the Top/Bottom:**
\[
A = \pi r^2
\]
**To Minimize the Cost of the Can:**
- **Radius of the can:** \_\_\_\_\_\_\_
- **Height of the can:** \_\_\_\_\_\_\_
- **Minimum cost:** \_\_\_\_\_\_ cents
Fill in the blanks with the appropriate values calculated using the above information and formulas to achieve minimum production cost.](https://content.bartleby.com/qna-images/question/9978ffa8-8e6a-4550-8363-e044b6a6e895/b0d000ad-72bc-4f7e-a53e-99d793a2565d/iknsugf_processed.png)
Transcribed Image Text:**Problem: Cost Minimization of a Cylinder Can**
A cylindrical can needs to be constructed to hold 250 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can needs to be thicker, costing 0.06 cents per square centimeter. Find the dimensions for the can that will minimize the production cost.
**Helpful Information:**
- \( h \): height of the can
- \( r \): radius of the can
**Formulas:**
1. **Volume of a Cylinder:**
\[
V = \pi r^2 h
\]
2. **Area of the Sides:**
\[
A = 2 \pi r h
\]
3. **Area of the Top/Bottom:**
\[
A = \pi r^2
\]
**To Minimize the Cost of the Can:**
- **Radius of the can:** \_\_\_\_\_\_\_
- **Height of the can:** \_\_\_\_\_\_\_
- **Minimum cost:** \_\_\_\_\_\_ cents
Fill in the blanks with the appropriate values calculated using the above information and formulas to achieve minimum production cost.
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