Homework Help is Here – Start Your Trial Now!
Math
Probability
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)
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...
See similar textbooks
icon
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.
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:

Cx=50+8000x+0.02x2

C¯x=Cxx

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer