Question

The total cost function for a product is C(x) = 750 ln(x + 10) + 1700 where x is the number of units produced. (a) Find the total cost of producing 300 units.

Answer 1

The total cost of producing 300 units, using the function C(x) = 750 ln(x + 10) + 1700, is calculated by substituting x with 300 and simplifying, which results in an approximate total cost of $6002.429.

Step-by-step explanation:

The student is asking to calculate the total cost of producing 300 units using the given cost function C(x) = 750 ln(x + 10) + 1700. To find the total cost, we substitute x with 300 in the function:

C(300) = 750 ln(300 + 10) + 1700

Which simplifies to:

C(300) = 750 ln(310) + 1700

Using a calculator, we find that ln(310) is approximately 5.736572. Plugging this value into the equation, we get:

C(300) = 750 × 5.736572 + 1700

This will give us:

C(300) = 4302.429 + 1700

Thus, the total cost of producing 300 units is approximately:

C(300) = $6002.429