Suppose that the number of crates of an agricultural product is given by 11xy-0.0002x² - 5y Z= 0.03x + 4y where x is the number of hours of labor and y is the number of acres of the crop. Find the marginal productivity of the number of hours of labor (x) when x = 200 and y = 400. (Round your answer to two decimal places.) crates Interpret your answer. ○ If 200 acres are planted, the expected change in the productivity for the 401st hour of labor is this many crates. ○ If 400 acres are planted, the expected change in the productivity for the 201st hour of labor is this many crates. If 400 acres are planted and 200 hours are worked, this is the number of crates produced. ○ If 200 acres are planted and 400 hours are worked, this is the number of crates produced.
Suppose that the number of crates of an agricultural product is given by 11xy-0.0002x² - 5y Z= 0.03x + 4y where x is the number of hours of labor and y is the number of acres of the crop. Find the marginal productivity of the number of hours of labor (x) when x = 200 and y = 400. (Round your answer to two decimal places.) crates Interpret your answer. ○ If 200 acres are planted, the expected change in the productivity for the 401st hour of labor is this many crates. ○ If 400 acres are planted, the expected change in the productivity for the 201st hour of labor is this many crates. If 400 acres are planted and 200 hours are worked, this is the number of crates produced. ○ If 200 acres are planted and 400 hours are worked, this is the number of crates produced.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Marginal Productivity in Agricultural Production
---
#### Problem Statement
Suppose that the number of crates of an agricultural product is given by the equation:
\[ z = \frac{11xy - 0.0002x^2 - 5y}{0.03x + 4y} \]
where \( x \) is the number of hours of labor and \( y \) is the number of acres of the crop.
#### Task
Find the marginal productivity of the number of hours of labor (\( x \)) when \( x = 200 \) and \( y = 400 \). (Round your answer to two decimal places.)
\[ \text{Marginal productivity} = \_\_\_\_\_\_ \text{ crates} \]
#### Answer Interpretation
- If 200 acres are planted, the expected change in the productivity for the 401st hour of labor is this many crates.
- If 400 acres are planted, the expected change in the productivity for the 201st hour of labor is this many crates.
- If 400 acres are planted and 200 hours are worked, this is the number of crates produced.
- If 200 acres are planted and 400 hours are worked, this is the number of crates produced.
---
The given equation represents a relationship between the number of hours of labor, the number of acres of crop planted, and the resulting number of crates produced. Students are required to calculate the marginal productivity for the given parameters and interpret the results accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8747d92-b055-4562-9504-cd72cffb1b1f%2Fb30ac1f4-b1f1-43ef-b1cb-cc237bd3395c%2Fwrd2fj_processed.png&w=3840&q=75)
Transcribed Image Text:### Marginal Productivity in Agricultural Production
---
#### Problem Statement
Suppose that the number of crates of an agricultural product is given by the equation:
\[ z = \frac{11xy - 0.0002x^2 - 5y}{0.03x + 4y} \]
where \( x \) is the number of hours of labor and \( y \) is the number of acres of the crop.
#### Task
Find the marginal productivity of the number of hours of labor (\( x \)) when \( x = 200 \) and \( y = 400 \). (Round your answer to two decimal places.)
\[ \text{Marginal productivity} = \_\_\_\_\_\_ \text{ crates} \]
#### Answer Interpretation
- If 200 acres are planted, the expected change in the productivity for the 401st hour of labor is this many crates.
- If 400 acres are planted, the expected change in the productivity for the 201st hour of labor is this many crates.
- If 400 acres are planted and 200 hours are worked, this is the number of crates produced.
- If 200 acres are planted and 400 hours are worked, this is the number of crates produced.
---
The given equation represents a relationship between the number of hours of labor, the number of acres of crop planted, and the resulting number of crates produced. Students are required to calculate the marginal productivity for the given parameters and interpret the results accordingly.
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