Maximizing Corral Area Using Calculus

The video tutorial explains how to use calculus to maximize the area of three identical corrals using 112 feet of fencing. The problem is set up by defining variables for the fence lengths and formulating constraint and primary equations. Calculus techniques, including finding derivatives, are used to determine the dimensions that maximize the area. The final solution provides the total dimensions and the dimensions of each individual corral.

What is the main objective of the problem discussed in the video?

• To determine the height of the barn

• To minimize the cost of fencing

• To maximize the area of three identical corrals

• To calculate the perimeter of a single corral

What is the total length of fencing available for the corrals?

• 100 feet

• 120 feet

• 112 feet

• 150 feet

What variable is assigned to the horizontal lengths of the corrals?

• Y

• Z

• X

• W

What is the constraint equation derived from the total fencing available?

• Y + 2X = 112

• Y + 5X = 112

• Y + 4X = 112

• Y + 3X = 112

What is the primary equation for the area of the corrals?

• Area = X - Y

• Area = X * Y

• Area = X / Y

• Area = X + Y

How is the primary equation expressed in terms of a single variable?

• By substituting Y = 112 - 4X

• By substituting X = 112 - 4Y

• By substituting Y = 112 - 3X

• By substituting X = 112 - 3Y

What is the derivative of the area equation with respect to X?

• 112 - 8X

• 112 + 8X

• 112 - 4X

• 112 + 4X

What is the value of X that maximizes the area?

• 12

• 18

• 14

• 16

What are the total dimensions that maximize the corral areas?

• 16 feet by 56 feet

• 12 feet by 56 feet

• 14 feet by 56 feet

• 18 feet by 56 feet

What are the dimensions of each individual corral?

• 14 feet by 18 feet 6 inches

• 14 feet by 18 feet 2 inches

• 14 feet by 18 feet 8 inches

• 14 feet by 18 feet 4 inches