Understanding Fiber Production and Partial Derivatives

The video tutorial explains how to calculate the weekly production of acetate fibers at an Oregon fiber manufacturing facility using a function of skilled and unskilled workers. It demonstrates evaluating the function for specific worker numbers and finding partial derivatives to understand the rate of change in output with respect to skilled and unskilled workers. The tutorial highlights the application of partial derivatives in real-world scenarios.

What is the function used to estimate the weekly production of acetate fibers?

• z = f(x, y)

• z = x + y

• z = x * y

• z = x - y

How many skilled workers are used in the calculation of fiber production?

• 10

• 13

• 11

• 12

What is the calculated weekly production of fibers with 11 skilled and 36 unskilled workers?

• 300,000 pounds

• 305,337 pounds

• 310,000 pounds

• 315,000 pounds

What is the partial derivative of the function with respect to skilled workers?

• 12,500 + 14xy - 15x^2

• 12,500 + 14x - 15y^2

• 12,500 + 14y - 15x^2

• 12,500 + 14xy + 15x^2

What is the rate of change of output with respect to skilled workers when x = 11 and y = 36?

• 1,800 pounds per skilled worker

• 1,500 pounds per skilled worker

• 1,629 pounds per skilled worker

• 1,700 pounds per skilled worker

What is the partial derivative of the function with respect to unskilled workers?

• 4,000 + 7x

• 4,000 + 7x^2

• 4,000 + 7xy

• 4,000 + 7y^2

What is the rate of change of output with respect to unskilled workers when x = 11 and y = 36?

• 4,847 pounds per unskilled worker

• 4,500 pounds per unskilled worker

• 5,000 pounds per unskilled worker

• 5,200 pounds per unskilled worker

What is the derivative of 4,000y with respect to y?

• 4,000

• 0

• y

• 4,000y

What is the derivative of 7x^2y with respect to y?

• 7x^2

• 7xy

• 7y

• 7x

Why are partial derivatives useful in this context?

• They help in understanding the rate of change of production with respect to different types of workers.

• They help in calculating total production.

• They help in reducing the number of workers.

• They help in increasing the number of workers.