Explanation Given Information: The fruit yield per tree in an orchard containing 50 trees is 100 pounds per tree each year. Because of crowding, the yield decreases by 1 pound per season for additional tree planted. Formula used: Steps to solve optimization problems: Step 1: Identify the unknowns with the aid of diagram. Step 2: Identify the objective function, the quantity to maximize or minimize. Step 3: Identify the constraint, the equations relating variables or inequalities expressing limitations on the value of the variables. Step 4: State the optimization problem Step 5: Eliminate the extra variables, solve the constraint for one unknown and substitute in the objective function. Step 6: Find the absolute maximum or absolute minimum of the objective function. Calculation: As it is provided that the fruit yield per tree in an orchard containing 50 trees is 100 pounds per tree each year. Because of crowding, the yield decreases by 1 pound per season for additional tree planted. Thus, let y ( x ) be the annual yield per tree for x trees planted. Then, y ( x ) = 100 − ( x − 50 ) = 150 − x Also, if Y ( x ) represents the total annual yield from x trees, then, Y ( x )

Finite Mathematics and Applied Calculus (MindTap Course List)

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ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 12.2, Problem 75E

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To calculate: The number of additional trees that should be planted for a maximum total annual yield if the fruit yield per tree in an orchard containing 50 trees is 100 pounds per tree each year. Because of crowding, the yield decreases by 1 pound per season for additional tree planted.

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Chapter 12.2, Problem 74E

Chapter 12.2, Problem 76E

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The number of additional trees that should be planted for a maximum total annual yield if the fruit yield per tree in an orchard containing 50 trees is 100 pounds per tree each year. Because of crowding, the yield decreases by 1 pound per season for additional tree planted.

Solution Summary: The author calculates the number of additional trees that should be planted for a maximum total annual yield if the fruit yield in an orchard containing 50 trees is 100 pounds per year.

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To calculate: The number of additional trees that should be planted for a maximum total annual yield if the fruit yield per tree in an orchard containing 50 trees is 100 pounds per tree each year. Because of crowding, the yield decreases by 1 pound per season for additional tree planted.

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Chapter 12 Solutions