cost for each site based on different output levels:

Output Level Austin Nashville Oklahoma City

$0250000100000360000$

$10000310000200000390000$

$20000370000300000420000$

$30000430000400000450000$

$40000490000500000480000$

$50000550000600000510000$

The optimal output range for each site is the range where the marginal cost of producing one more unit is less than the revenue generated by that unit. This is also known as the range of increasing returns to scale. In other words, it is the range where the total cost per unit decreases as output increases.

Based on the table above, we can see that Austin has the lowest fixed cost and variable cost per unit, making it the most cost$-$effective site for producing up to $50,000$ units. Nashville has a higher fixed cost but a lower variable cost per unit, making it more suitable for producing between $20,000$ and $40,000$ units. Oklahoma City has the highest fixed cost but the lowest variable cost per unit, making it more suitable for producing between $30,000$ and $50,000$ units