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4.8: Applied Optimization Problems

https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2410%3A_Calculus_(Open_Stax)_Novick/04%3A_Applications_of_Derivatives/4.08%3A_Applied_Optimization_Problems

One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it i...One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it is often desirable to minimize the amount of material used to package a product with a certain volume. In this section, we show how to set up these types of minimization and maximization problems and solve them by using the tools developed in this chapter.

4.7: Optimization Problems

https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT301_Calculus_I/04%3A_Applications_of_Derivatives/4.07%3A_Optimization_Problems

Solution: Let

$x$ denote the length of the side of the garden perpendicular to the rock wall and

$y$ denote the length of the side parallel to the rock wall. Suppose the cost of the material for t...Solution: Let

$x$ denote the length of the side of the garden perpendicular to the rock wall and

$y$ denote the length of the side parallel to the rock wall. Suppose the cost of the material for the base is

$20¢/in.^2$ and the cost of the material for the sides is

$30¢/in.^2$ and we are trying to minimize the cost of this box. Write the cost as a function of the side lengths of the base. (Let

$x$ be the side length of the base and

$y$ be the height of the box.)

3.10: Applied Optimization Problems

https://math.libretexts.org/Courses/Southwestern_College/Business_Calculus/03%3A_Unit_3_-_Derivatives/3.10%3A_Applied_Optimization_Problems

One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it i...One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it is often desirable to minimize the amount of material used to package a product with a certain volume. In this section, we show how to set up these types of minimization and maximization problems and solve them by using the tools developed in this chapter.

4.5: Optimization Problems

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/Chapter_4%3A_Applications_of_Derivatives/4.5%3A_Optimization_Problems

Solution: Let

$x$ denote the length of the side of the garden perpendicular to the rock wall and

$y$ denote the length of the side parallel to the rock wall. Suppose the cost of the material for t...Solution: Let

$x$ denote the length of the side of the garden perpendicular to the rock wall and

$y$ denote the length of the side parallel to the rock wall. Suppose the cost of the material for the base is

$20¢/in.^2$ and the cost of the material for the sides is

$30¢/in.^2$ and we are trying to minimize the cost of this box. Write the cost as a function of the side lengths of the base. (Let

$x$ be the side length of the base and

$y$ be the height of the box.)

4.8: Applied Optimization Problems

https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/04%3A_Applications_of_Derivatives/4.08%3A_Applied_Optimization_Problems

One common application of calculus is calculating the minimum or maximum value of a function subject to some constraint on its input or output. For example, in manufacturing, it is often desirable to ...One common application of calculus is calculating the minimum or maximum value of a function subject to some constraint on its input or output. For example, in manufacturing, it is often desirable to minimize the amount of material used to package a product with a certain volume. In this section, we show how to set up these types of minimization and maximization problems and solve them by using the tools developed in this chapter.

4.5: Applied Optimization Problems

https://math.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/Math_140%3A_Calculus_1_(Gaydos)/04%3A_Applications_of_Derivatives/4.05%3A_Applied_Optimization_Problems

One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it i...One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it is often desirable to minimize the amount of material used to package a product with a certain volume. In this section, we show how to set up these types of minimization and maximization problems and solve them by using the tools developed in this chapter.

4.4: Optimization Problems

https://math.libretexts.org/Courses/Chabot_College/MTH_1%3A_Calculus_I/04%3A_Applications_of_Derivatives/4.04%3A_Optimization_Problems

One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it i...One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it is often desirable to minimize the amount of material used to package a product with a certain volume. In this section, we show how to set up these types of minimization and maximization problems and solve them by using the tools developed in this chapter.

4.7: Applied Optimization Problems

https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/04%3A_Applications_of_Derivatives/4.07%3A_Applied_Optimization_Problems

One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it i...One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it is often desirable to minimize the amount of material used to package a product with a certain volume. In this section, we show how to set up these types of minimization and maximization problems and solve them by using the tools developed in this chapter.

4.8: Applied Optimization Problems

https://math.libretexts.org/Courses/Mission_College/MAT_003A_Calculus_I_(Fineman)/04%3A_Applications_of_Derivatives/4.08%3A_Applied_Optimization_Problems

One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it i...One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it is often desirable to minimize the amount of material used to package a product with a certain volume. In this section, we show how to set up these types of minimization and maximization problems and solve them by using the tools developed in this chapter.

4.5: Optimization Problems

https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_hdagnew@ucdavis.edu/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2%2F%2FChapter_4%3A_Applications_of_Derivatives/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2%2F%2FChapter_4%3A_Applications_of_Derivatives%2F%2F4.5%3A_Optimization_Problems

Solution: Let

$x$ denote the length of the side of the garden perpendicular to the rock wall and

$y$ denote the length of the side parallel to the rock wall. Suppose the cost of the material for t...Solution: Let

$x$ denote the length of the side of the garden perpendicular to the rock wall and

$y$ denote the length of the side parallel to the rock wall. Suppose the cost of the material for the base is

$20¢/in.^2$ and the cost of the material for the sides is

$30¢/in.^2$ and we are trying to minimize the cost of this box. Write the cost as a function of the side lengths of the base. (Let

$x$ be the side length of the base and

$y$ be the height of the box.)

4.6: Applied Optimization Problems

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Seeburger)/04%3A_Applications_of_Derivatives/4.06%3A_Applied_Optimization_Problems

One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it i...One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it is often desirable to minimize the amount of material used to package a product with a certain volume. In this section, we show how to set up these types of minimization and maximization problems and solve them by using the tools developed in this chapter.

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