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Calculus I (Practice Problems) / Applications of Derivatives / Optimization   [Notes] [Practice Problems] [Assignment Problems]

Calculus I - Practice Problems
Derivatives Previous Chapter   Next Chapter Integrals
The Mean Value Theorem Previous Section   Next Section More Optimization Problems

1. Find two positive numbers whose sum is 300 and whose product is a maximum. [Solution]

 

2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other is a minimum. [Solution]

 

3. Let x and y be two positive numbers such that  and  is a maximum. [Solution]

 

4. We are going to fence in a rectangular field.  If we look at the field from above the cost of the vertical sides are $10/ft, the cost of the bottom is $2/ft and the cost of the top is $7/ft.  If we have $700 determine the dimensions of the field that will maximize the enclosed area. [Solution]

 

5. We have 45 m2 of material to build a box with a square base and no top.  Determine the dimensions of the box that will maximize the enclosed volume. [Solution]

 

6. We want to build a box whose base length is 6 times the base width and the box will enclose 20 in3.  The cost of the material of the sides is $3/in2 and the cost of the top and bottom is $15/in2.  Determine the dimensions of the box that will minimize the cost. [Solution]

 

7. We want to construct a cylindrical can with a bottom but no top that will have a volume of 30 cm3.  Determine the dimensions of the can that will minimize the amount of material needed to construct the can. [Solution]

 

8. We have a piece of cardboard that is 50 cm by 20 cm and we are going to cut out the corners and fold up the sides to form a box.  Determine the height of the box that will give a maximum volume. [Solution]

 

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The Mean Value Theorem Previous Section   Next Section More Optimization Problems
Derivatives Previous Chapter   Next Chapter Integrals

Calculus I (Practice Problems) / Applications of Derivatives / Optimization    [Notes] [Practice Problems] [Assignment Problems]

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