Final answer:
The average profit per mower if 20 mowers are produced is $30.5. The marginal average profit at a production level of 20 mowers is $39.2. The average profit per mower if 21 mowers are produced can be estimated as $69.7.
Step-by-step explanation:
In order to find the average profit per mower if 20 mowers are produced, we need to substitute x = 20 into the given profit function P(x) = 40x - 0.02x^2 - 450.
So, P(20) = 40(20) - 0.02(20)^2 - 450 = $<<40*20 - 0.02*20^2 - 450=610>>610.
Therefore, the average profit per mower if 20 mowers are produced is $610/20 = $<<610/20=30.5>>30.5.
To find the marginal average profit at a production level of 20 mowers, we need to find the derivative of the profit function with respect to x.
P'(x) = 40 - 0.04x.
Substituting x = 20 into the derivative, we get P'(20) = 40 - 0.04(20) = 40 - 0.8 = 39.2.
Therefore, the marginal average profit at a production level of 20 mowers is $39.2.
Using the results from parts A and B, we can estimate the average profit per mower if 21 mowers are produced.
We know that the average profit per mower if 20 mowers are produced is $30.5. Since the marginal average profit is 39.2, the additional profit made by producing one more mower is $39.2.
Hence, the average profit per mower if 21 mowers are produced can be estimated as $30.5 + $39.2 = $69.7.