The profit (in dollars) from the sale of lawn mowers is .
(A) Find the average profit per mower if 50 mowers are produced.
(B) Find the marginal average profit at a production level of 50 mowers, and interpret the results.
© Use the results from parts (A) and (B) to estimate the average profit per mower if 51 mowers are produced.
(A) If 50 mowers are produced, the average profit per mower is .
(Round to the nearest cent as needed.)

Ask by Norton Olson. in the United States

Mar 30,2025

Question

The profit (in dollars) from the sale of lawn mowers is .
(A) Find the average profit per mower if 50 mowers are produced.
(B) Find the marginal average profit at a production level of 50 mowers, and interpret the results.
© Use the results from parts (A) and (B) to estimate the average profit per mower if 51 mowers are produced.
(A) If 50 mowers are produced, the average profit per mower is .
(Round to the nearest cent as needed.)

Ask by Norton Olson. in the United States

Mar 30,2025

UpStudy AI · Accepted Answer

To find the average profit per mower if 50 mowers are produced, we need to calculate the total profit from selling 50 mowers and then divide it by 50.

Given:
$$ P(x) = 70x - 0.07x^2 - 450 $$

To find the average profit per mower if 50 mowers are produced:
1. Calculate the total profit from selling 50 mowers:
$$ P(50) = 70(50) - 0.07(50)^2 - 450 $$
2. Divide the total profit by 50 to find the average profit per mower:
$$ \text{Average Profit} = \frac{P(50)}{50} $$

Let's calculate the average profit per mower if 50 mowers are produced.
Calculate the value by following steps:
- step0: Calculate:
  $$70\times 50-0.07\times 50^{2}-450$$
- step1: Multiply the numbers:
  $$3500-0.07\times 50^{2}-450$$
- step2: Multiply the numbers:
  $$3500-175-450$$
- step3: Subtract the numbers:
  $$2875$$
The total profit from selling 50 mowers is $2875.

Now, let's calculate the average profit per mower:
$$ \text{Average Profit} = \frac{2875}{50} = \$57.50 $$

Therefore, if 50 mowers are produced, the average profit per mower is $57.50.
If 50 mowers are produced, the average profit per mower is $57.50.

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