The profit (in dollars) from the sale of x lawn mowers is P(x)= 20x - 0.02x^2 - 650(A) Find the average profit per mower if 60 mowers are produced(B) Find the marginal average profit at production level of 60 mowers, and interpret results(C)Use the results from parts A and B to estimate the average profit per mower if 61 mowers are produced ( ### Problem StatementThe profit (in dollars) from the sale of $ x $ lawn mowers is given by the function $ P(x) = 20x - 0.02x^2 - 650 $.#### Tasks:**(A)** Find the average profit per mower if 60 mowers are produced.**(B)** Determine the marginal average profit at a production level of 60 mowers and interpret the results.**(C)** Using the results from parts (A) and (B), estimate the average profit per mower if 61 mowers are produced.### Solution Steps- **(A)** Calculate the average profit per mower when 60 mowers are produced. The formula for average profit per mower is $\frac{P(x)}{x}$.- **(B)** Find the derivative $ P'(x) $, which gives the marginal profit. Evaluate this derivative at $ x = 60 $ to find the marginal average profit.- **Interpretation of $ P'(60) = \$0.16 $ per mower:** - **Option A:** At a production level of 60 mowers, the average profit is $0.16 per mower. - **Option B:** At a production level of 60 mowers, a unit increase in production will increase the total profit by $0.16 per mower. - **Option C:** At a production level of 60 mowers, the average profit is increasing at a rate of $0.16 per mower.- **(C)** Using parts (A) and (B), estimate the average profit per mower if 61 mowers are produced. This involves using the calculated average profit for 60 mowers and adjusting it by the marginal average profit found in part (B).**Note:** Round to the nearest cent where needed.

Marginal Profit: We can quantify the rising in the profit when an increment in the number of sold…

The profit (in dollars) from the sale of x lawn mowers is P(x) = 20x -0.02x² - 650. (A) Find the average profit per mower if 60 mowers are produced. (B) Find the marginal average profit at a production level of 60 mowers, and interpret the results. (C) Use the results from parts (A) and (B) to estimate the average profit per mower if 61 mowers are produced. (A) If 60 mowers are produced, the average profit per mower is $ (Round to the nearest cent as needed.) (B) The marginal average profit at a production level of 60 units is $ (Round to the nearest cent as needed.) Choose the correct interpretation of P'(60) = $0.16 per mower. per mower. O A. At a production level of 60 mowers the average profit is $0.16 per mower. OB. At a production level of 60 mowers a unit increase in production will increase the total profit by $0.16 per mower. OC. At a production level of 60 mowers the average profit is increasing at a rate of $0.16 per mower. C) Using parts (A) and (B), the estimate of the average profit per mower if 61 mowers are produced is $ Round to the nearest cent as needed.)

The profit (in dollars) from the sale of x lawn mowers is P(x) = 20x -0.02x² - 650. (A) Find the average profit per mower if 60 mowers are produced. (B) Find the marginal average profit at a production level of 60 mowers, and interpret the results. (C) Use the results from parts (A) and (B) to estimate the average profit per mower if 61 mowers are produced. (A) If 60 mowers are produced, the average profit per mower is $ (Round to the nearest cent as needed.) (B) The marginal average profit at a production level of 60 units is $ (Round to the nearest cent as needed.) Choose the correct interpretation of P'(60) = $0.16 per mower. per mower. O A. At a production level of 60 mowers the average profit is $0.16 per mower. OB. At a production level of 60 mowers a unit increase in production will increase the total profit by $0.16 per mower. OC. At a production level of 60 mowers the average profit is increasing at a rate of $0.16 per mower. C) Using parts (A) and (B), the estimate of the average profit per mower if 61 mowers are produced is $ Round to the nearest cent as needed.)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

The profit (in dollars) from the sale of x lawn mowers is P(x)= 20x - 0.02x^2 - 650 (A) Find the average profit per mower if 60 mowers are produced (B) Find the marginal average profit at production level of 60 mowers, and interpret results (C)Use the results from parts A and B to estimate the average profit per mower if 61 mowers are produced (

### Problem Statement

The profit (in dollars) from the sale of $ x $ lawn mowers is given by the function $ P(x) = 20x - 0.02x^2 - 650 $.

#### Tasks:

**(A)** Find the average profit per mower if 60 mowers are produced.

**(B)** Determine the marginal average profit at a production level of 60 mowers and interpret the results.

**(C)** Using the results from parts (A) and (B), estimate the average profit per mower if 61 mowers are produced.

### Solution Steps

- **(A)** Calculate the average profit per mower when 60 mowers are produced. The formula for average profit per mower is $\frac{P(x)}{x}$.

- **(B)** Find the derivative $ P'(x) $, which gives the marginal profit. Evaluate this derivative at $ x = 60 $ to find the marginal average profit.

- **Interpretation of $ P'(60) = \$0.16 $ per mower:**

- **Option A:** At a production level of 60 mowers, the average profit is $0.16 per mower.
- **Option B:** At a production level of 60 mowers, a unit increase in production will increase the total profit by $0.16 per mower.
- **Option C:** At a production level of 60 mowers, the average profit is increasing at a rate of $0.16 per mower.

- **(C)** Using parts (A) and (B), estimate the average profit per mower if 61 mowers are produced. This involves using the calculated average profit for 60 mowers and adjusting it by the marginal average profit found in part (B).

**Note:** Round to the nearest cent where needed.

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