Questions: Question 18.1.4.61-BE Part 1 of 4: A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation C(x) = 9.0004(x - 200)^4 + 246,840 for 100 ≤ x ≤ 1,000 where C(x) is the cost in dollars for handling x cases per month. The average cost per case is given by C(x) = C(x) / x. Complete parts (A) through (C) (A) Write the equation for the average cost function C̅

Question 18.1.4.61-BE Part 1 of 4:

A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation
C(x) = 9.0004(x - 200)^4 + 246,840 for 100 ≤ x ≤ 1,000

where C(x) is the cost in dollars for handling x cases per month. The average cost per case is given by C(x) = C(x) / x. Complete parts (A) through (C)

(A) Write the equation for the average cost function C̅

Transcript text: The image contains text information along with a mathematical expression involving a cost equation. The text content extracted from the image is: Question 18.1.4.61-BE Part 1 of 4: A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation C(x) = 9.0004(x - 200)^4 + 246,840 / 100 ≤ x ≤ 1,000 where C(x) is the cost in dollars for handling x cases per month. The average cost per case is given by C(x) = C(x) / x. Complete parts (A) through (C) (A) Write the equation for the average cost function C̅

Solution

Solution Steps

Step 1: Identify the given cost function

The given cost function is \( C(x) = 0.1x^2 + 200 \).

Step 2: Define the average cost function

The average cost function \( \overline{C}(x) \) is defined as the total cost divided by the number of cases, \( x \). Therefore, \( \overline{C}(x) = \frac{C(x)}{x} \).

Step 3: Substitute the given cost function into the average cost function

Substitute \( C(x) = 0.1x^2 + 200 \) into \( \overline{C}(x) \): \[ \overline{C}(x) = \frac{0.1x^2 + 200}{x} \]