Final answer:
The total cost of producing 200 units is approximately $5,231.50. The number of units that will result in total costs of $9,500 is approximately 6216 units.
Step-by-step explanation:
To find the total cost of producing 200 units, we need to substitute x = 200 into the total cost function C(x).
Plugging in the value, we have:
C(200) = 875 ln(200 + 10) + 1900
Using a calculator, we can evaluate the natural logarithm to get:
C(200) ≈ 875 ln(210) + 1900
Finally, we can calculate the total cost by evaluating the expression:
C(200) ≈ 875(5.34) + 1900 ≈ $5,231.50
Therefore, the total cost of producing 200 units is approximately $5,231.50.
To determine the number of units that will result in total costs of $9,500, we need to solve the equation C(x) = 9500 for x. Rearranging the equation, we have:
875 ln(x + 10) + 1900 = 9500
Subtracting 1900 from both sides:
875 ln(x + 10) = 7600
Dividing both sides by 875:
ln(x + 10) = 8.6857
Taking the natural logarithm of both sides gives:
x + 10 = e^8.6857
Subtracting 10 from both sides:
x = e^8.6857 - 10
Using a calculator, we can compute:
x ≈ 6225.74 - 10 ≈ 6215.74
Rounding to the nearest whole number, the number of units that will result in total costs of $9500 is approximately 6216 units.