Final answer:
To find the marginal cost of producing the 10th item, calculate the change in total cost when the quantity changes from 9 to 10. The marginal cost is 106 dollars. It represents the additional cost incurred when producing one additional item.
Step-by-step explanation:
To find the marginal cost of producing the 10th item, we need to calculate the change in total cost when the quantity changes from 9 to 10. The total cost function is C(q) = 1000 + 2q^2 dollars. So, the total cost of producing 10 items is C(10) = 1000 + 2(10)^2 = 1200 dollars. Now, we calculate the total cost of producing 9 items: C(9) = 1000 + 2(9)^2 = 1094 dollars.
The change in total cost is 1200 - 1094 = 106 dollars. Since we are going from 9 to 10 items, the change in quantity is 1. Therefore, the marginal cost of producing the 10th item is 106 dollars.
Interpreting the answer in terms of costs, the marginal cost represents the additional cost incurred when producing one additional item. In this case, the marginal cost of producing the 10th item is 106 dollars. This means that the cost to produce the 10th item is 106 dollars more than the cost to produce the 9th item.