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.

### (C) Interpret the Slope and Y-Intercept of the Cost Equation

From the equation $C(x) = 175x - 8,353$:

- **Slope $m = 175$:** This represents the **marginal cost** of producing each additional golf club. For every extra golf club produced, the cost increases by $175. This is the variable cost per unit.

- **Y-intercept $b = -8,353$:** This represents the **fixed cost** when no golf clubs are produced. The negative value of $-8,353$ suggests that there are initial losses or costs that must be offset before production becomes profitable. It could imply initial investment or fixed costs that don't cover all expenses for low production levels.

Do you have any further questions on this analysis or need more details?

Here are 5 related questions to deepen your understanding:

1. How would the cost equation change if the marginal cost increased to $200 per club?
2. What would be the breakeven point where the total daily cost equals zero?
3. How would the interpretation of the fixed cost change if it were positive?
4. If the cost to produce 150 clubs is known, can you confirm the cost function is linear?
5. How can you use this model to predict the cost for large-scale production, say 500 clubs per day?

**Tip:** When analyzing linear cost functions, the slope always tells you the per-unit increase in cost, and the intercept reflects the cost at zero production.

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.

Learn how to analyze the cost of producing golf clubs using linear equations. This problem involves calculating the total daily cost for producing x golf clubs based on given data points for 80 and 100 units. Understand the interpretation of the slope and y-intercept in a real-world cost equation. Suitable for students in Grades 9-12.

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