Final answer:
To determine the total cost of producing 200 units, we plug x=200 into the total cost function C(x) = 700 ln(x + 10) + 1600. After calculating, we find the total cost to be approximately $5342.98, rounded to the nearest cent.
Step-by-step explanation:
To find the total cost of producing 200 units, we need to use the total cost function C(x) = 700 ln(x + 10) + 1600 given in the question. We simply plug in 200 for x in the function and perform the calculations.
We calculate the natural logarithm of (200 + 10), which is ln(210), and then multiply it by 700. After finding this value, we add the fixed cost of 1600 to get the total cost:
- C(200) = 700 ln(200 + 10) + 1600
- C(200) = 700 ln(210) + 1600
- C(200) = 700 * ln(210) + 1600
Using a calculator, we find that ln(210) is approximately 5.347108. So, the calculation for the total cost is:
- C(200) = 700 * 5.347108 + 1600
- C(200) = 3742.9756 + 1600
- C(200) = 5342.9756
Therefore, the total cost to produce 200 units is approximately $5342.98, rounded to the nearest cent.