Cost analysis. A plant can manufacture 80 golf clubs perday for a total daily cost of 57,647 and 100 golf clubs per day for a total daily cost of $9,147. 
(A) Assuming that daily cost and production are linearly related, find the total daily cost of producing x golf clubs.
( B) Graph the total daily cost for 0 <= x <= 200
(C) Interpret the slope and y intercept of this cost equation.

Here is the graph of the total daily cost function $ C(x) = 175x - 8353 $ for producing golf clubs, with the range $ 0 \leq x \leq 200 $.

### Part (C) Interpreting the slope and y-intercept:

- **Slope (175):** The slope represents the **variable cost per golf club**. This means that for each additional golf club produced, the total cost increases by \$175.
  
- **Y-intercept (-8353):** The y-intercept represents the **fixed costs**, which is the total cost when no golf clubs are produced. In this case, the y-intercept is negative (\$-8353), suggesting that certain fixed costs (or initial overhead) are offset by other factors not directly related to production.

Would you like further clarification on any part of the solution? Here are five related questions to explore:

1. How would the cost function change if the fixed costs were higher?
2. What if the slope of the cost function was lower—what would that mean for production costs?
3. How can you determine the break-even point using the cost function?
4. What would be the impact of increasing production beyond 200 golf clubs?
5. Can this cost model be applied to other manufacturing processes?

**Tip:** Understanding the slope of a linear equation is essential in cost analysis—it directly reflects how much your cost will rise with each unit produced!

Cost analysis. A plant can manufacture 80 golf clubs per day for a total daily cost of $5,647 and 100 golf clubs per day for a total daily cost of $9,147. (A) Assuming that daily cost and production are linearly related, find the total daily cost of producing x golf clubs. (B) Graph the total daily cost for 0 <= x <= 200. (C) Interpret the slope and y intercept of this cost equation.

Analyze the linear cost function of a plant producing 80-100 golf clubs daily. Learn how to calculate the total daily cost for any number of clubs, graph the cost function for 0 <= x <= 200, and interpret the slope and y-intercept of the equation. This problem covers linear equations and cost analysis, suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation