A commercial vegetable and fruit grower carefully observes the relationship between the amount of fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting pumpkin crop, recorded in the following table Amount of Fertilizer |250 500 750 1000 1250 1500 1750 2000 (pounds/acre) --- Revenue earned 96 145 172 185 192 196 198 199 (dollars/acre) The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount of fertilizer to use? Check your advice by answering/calculating the following. • Is cach pound of fertilizer equally effective? Explain. • Graph the data and then estimate the maximum amount of revenue that can be earned per acre from your graph. Call this estimate c. • Compute a linear regression for the data. • Compute a logarithmic regression(LnReg) for the data. • Use trial and error on your calculator to fit a function of the form r = c(1 – b") where c is the estimate for the maximum amount of revenue and 0 < b < 1 • Choose the best model for revenue and then write a total cost function for fertilizer. Use graphs on your calculator to find where cost equals revenue. • Write a profit function and graph it to advise the grower on the most profitable amount of fertilizer to use.
A commercial vegetable and fruit grower carefully observes the relationship between the amount of fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting pumpkin crop, recorded in the following table Amount of Fertilizer |250 500 750 1000 1250 1500 1750 2000 (pounds/acre) --- Revenue earned 96 145 172 185 192 196 198 199 (dollars/acre) The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount of fertilizer to use? Check your advice by answering/calculating the following. • Is cach pound of fertilizer equally effective? Explain. • Graph the data and then estimate the maximum amount of revenue that can be earned per acre from your graph. Call this estimate c. • Compute a linear regression for the data. • Compute a logarithmic regression(LnReg) for the data. • Use trial and error on your calculator to fit a function of the form r = c(1 – b") where c is the estimate for the maximum amount of revenue and 0 < b < 1 • Choose the best model for revenue and then write a total cost function for fertilizer. Use graphs on your calculator to find where cost equals revenue. • Write a profit function and graph it to advise the grower on the most profitable amount of fertilizer to use.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Write a profit function and graph it to advise the grower on the most profitable amount of fertilizer to use.
Transcribed Image Text:A commercial vegetable and fruit grower carefully observes the relationship between the amount of
fertilizer used on a certain variety of pumpkin and the revenue made from sales of the resulting
pumpkin crop, recorded in the following table
Amount of
Fertilizer
|250 500 750 1000 1250 1500 1750 2000
(pounds/acre)
---
Revenue
earned
96 145 172 185 192 196 198
199
(dollars/acre)
The fertilizer costs $0.14 per pound. What would you advise the grower is the most profitable amount
of fertilizer to use? Check your advice by answering/calculating the following.
• Is cach pound of fertilizer equally effective? Explain.
• Graph the data and then estimate the maximum amount of revenue that can be earned per acre
from your graph. Call this estimate c.
• Compute a linear regression for the data.
• Compute a logarithmic regression(LnReg) for the data.
• Use trial and error on your calculator to fit a function of the form r = c(1 – b") where c is
the estimate for the maximum amount of revenue and 0 < b < 1
• Choose the best model for revenue and then write a total cost function for fertilizer. Use graphs
on your calculator to find where cost equals revenue.
• Write a profit function and graph it to advise the grower on the most profitable amount of
fertilizer to use.
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