Answer :
To find the total cost of producing 32 pizza ovens, we need to consider both the fixed cost and the marginal cost for each oven.
1. Fixed Cost:
The fixed cost is the cost you incur regardless of how many ovens you produce. Here, the fixed cost is [tex]$8,000.00.
2. Marginal Cost:
The marginal cost is the additional cost of producing one more oven. It is given by the function \( C'(x) = \frac{2000}{x} \), where \( x \) is the number of ovens.
3. Calculating Total Marginal Cost for 32 Ovens:
To find the total marginal cost, we need to add up the marginal costs for each individual oven from the 1st to the 32nd oven. This means we calculate:
\[
\text{Total Marginal Cost} = \sum_{x=1}^{32} \frac{2000}{x}
\]
This calculation involves summing up the values of the function \( \frac{2000}{x} \) as \( x \) takes each integer value from 1 to 32.
4. Total Cost:
Once we have the total marginal cost, we add it to the fixed cost to get the total cost:
\[
\text{Total Cost} = \text{Fixed Cost} + \text{Total Marginal Cost}
\]
5. Result:
After performing these calculations, the total cost to produce 32 pizza ovens comes out to be rounded to two decimal places:
\[
\$[/tex] 16,116.99
\]
Therefore, based on these calculations, the correct answer is that the total cost to produce 32 pizza ovens is closest to:
B. \$ 16,486.46
1. Fixed Cost:
The fixed cost is the cost you incur regardless of how many ovens you produce. Here, the fixed cost is [tex]$8,000.00.
2. Marginal Cost:
The marginal cost is the additional cost of producing one more oven. It is given by the function \( C'(x) = \frac{2000}{x} \), where \( x \) is the number of ovens.
3. Calculating Total Marginal Cost for 32 Ovens:
To find the total marginal cost, we need to add up the marginal costs for each individual oven from the 1st to the 32nd oven. This means we calculate:
\[
\text{Total Marginal Cost} = \sum_{x=1}^{32} \frac{2000}{x}
\]
This calculation involves summing up the values of the function \( \frac{2000}{x} \) as \( x \) takes each integer value from 1 to 32.
4. Total Cost:
Once we have the total marginal cost, we add it to the fixed cost to get the total cost:
\[
\text{Total Cost} = \text{Fixed Cost} + \text{Total Marginal Cost}
\]
5. Result:
After performing these calculations, the total cost to produce 32 pizza ovens comes out to be rounded to two decimal places:
\[
\$[/tex] 16,116.99
\]
Therefore, based on these calculations, the correct answer is that the total cost to produce 32 pizza ovens is closest to:
B. \$ 16,486.46
