We are given that the cost to air x 30-second commercials during the value of x that minimizes the average cost, so the first step cost per commercial. C(x) = C(x) X a football game can be approximated by the function C(x) = 50 +8,000x + 0.02x² thousand dollars. We are asked to find C(x) to find the function that describes the average cost. Recall that the average cost is given by C(x) = Find the average X
We are given that the cost to air x 30-second commercials during the value of x that minimizes the average cost, so the first step cost per commercial. C(x) = C(x) X a football game can be approximated by the function C(x) = 50 +8,000x + 0.02x² thousand dollars. We are asked to find C(x) to find the function that describes the average cost. Recall that the average cost is given by C(x) = Find the average X
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![We are given that the cost to air \( x \) 30-second commercials during a football game can be approximated by the function \( C(x) = 50 + 8,000x + 0.02x^2 \) thousand dollars. We are asked to find the value of \( x \) that minimizes the average cost, so the first step is to find the function that describes the average cost. Recall that the average cost is given by \( \overline{C}(x) = \frac{C(x)}{x} \). Find the average cost per commercial.
\[
\overline{C}(x) = \frac{C(x)}{x}
\]
\[
= \frac{\text{\textcolor{white}{empty box}}}{x}
\]
\[
= \frac{50}{x} + 8,000 + 0.02x
\]
Explanation of the Process:
1. **Function for Average Cost**: To find the average cost per commercial, we divide the total cost function \( C(x) \) by the number of commercials \( x \).
2. **Simplification**: The equation simplifies as follows:
- \( \frac{C(x)}{x} = \frac{50 + 8,000x + 0.02x^2}{x} \)
- Break down each term: \( \frac{50}{x} + \frac{8,000x}{x} + \frac{0.02x^2}{x} \)
- This leads to \( \frac{50}{x} + 8,000 + 0.02x \)
3. **Graph Layout**:
- No graphs or additional diagrams are provided. The focus is solely on algebraic manipulation to arrive at the average cost function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd48171ba-d1cc-47b1-bf9c-8041143384f0%2F1f64883d-f7ed-495c-b150-93f3d6cf2f49%2Fquv9vo_processed.png&w=3840&q=75)
Transcribed Image Text:We are given that the cost to air \( x \) 30-second commercials during a football game can be approximated by the function \( C(x) = 50 + 8,000x + 0.02x^2 \) thousand dollars. We are asked to find the value of \( x \) that minimizes the average cost, so the first step is to find the function that describes the average cost. Recall that the average cost is given by \( \overline{C}(x) = \frac{C(x)}{x} \). Find the average cost per commercial.
\[
\overline{C}(x) = \frac{C(x)}{x}
\]
\[
= \frac{\text{\textcolor{white}{empty box}}}{x}
\]
\[
= \frac{50}{x} + 8,000 + 0.02x
\]
Explanation of the Process:
1. **Function for Average Cost**: To find the average cost per commercial, we divide the total cost function \( C(x) \) by the number of commercials \( x \).
2. **Simplification**: The equation simplifies as follows:
- \( \frac{C(x)}{x} = \frac{50 + 8,000x + 0.02x^2}{x} \)
- Break down each term: \( \frac{50}{x} + \frac{8,000x}{x} + \frac{0.02x^2}{x} \)
- This leads to \( \frac{50}{x} + 8,000 + 0.02x \)
3. **Graph Layout**:
- No graphs or additional diagrams are provided. The focus is solely on algebraic manipulation to arrive at the average cost function.
Expert Solution
Step 1
Given function:
Step by step
Solved in 2 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON