Question

The total cost function for a product is given by: C(x) = 850ln (x+10) +1900 where x is the number of units produced. Find the total cost of producing 400 units. Please round your answer to the nearest whole number or decimal place as instructed.

Answer 1

To calculate the total cost of producing 400 units, substitute 400 into the total cost function, perform the operations, and round the result to the nearest whole number, resulting in approximately $7014.

Step-by-step explanation:

To find the total cost of producing 400 units using the given total cost function C(x) = 850ln (x+10) + 1900, we need to substitute x with 400 and calculate the value of C(400).

Firstly, let's substitute 400 into the function:
C(400) = 850ln (400+10) + 1900

Now, calculate the natural logarithm of 410 and then multiply by 850, and add 1900 to get the total cost.

Using a calculator, the natural logarithm of 410 is approximately 6.01616. So,
C(400) = 850 * 6.01616 + 1900

After performing the multiplication and addition, the total cost to produce 400 units is:
C(400) ≈ 850 * 6.01616 + 1900 ≈ 5113.736 + 1900 ≈ 7013.736

Rounded to the nearest whole number, the total cost is approximately $7014.

Answer 2

The total cost of producing 400 units is approximately $5,971.34.

Step-by-step explanation:

To find the total cost for producing 400 units, substitute x = 400 into the cost function C(x) = 850ln(x+10) + 1900. Begin by adding 10 to 400, resulting in 410 inside the natural logarithm.

Taking the natural logarithm of 410 gives approximately 6.018. Multiply this value by 850 to get around 5115.3. Adding 1900 to 5115.3 yields a total cost of roughly $7015.3.

However, the instruction is to round the answer. Hence, the cost, $7015.3, rounded to the nearest whole number or decimal place, when rounded to two decimal places, becomes $5971.34.

This is the total cost of producing 400 units according to the given cost function.