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Let's analyze and solve the given problem step-by-step:

### (a) Write down the associated linear cost, revenue, and profit functions.
The information provided includes:
- **Fixed production costs**: $68 per edition
- **Marginal printing and distribution cost**: $0.30 per copy
- **Selling price**: $0.40 per copy

Let $ x $ represent the number of copies of the newspaper.

1. **Cost function**: The total cost includes the fixed cost and the variable cost per copy.
   \[
   C(x) = 68 + 0.3x
   \]

2. **Revenue function**: The revenue is calculated by multiplying the number of copies sold by the selling price per copy.
   \[
   R(x) = 0.4x
   \]

3. **Profit function**: Profit is given by the difference between revenue and cost.
   \[
   P(x) = R(x) - C(x) = 0.4x - (68 + 0.3x) = 0.1x - 68
   \]

### (b) What profit (or loss) results from the sale of 300 copies?
Substitute $ x = 300 $ into the profit function:

\[
P(300) = 0.1(300) - 68 = 30 - 68 = -38
\]

This means a loss of $38 when selling 300 copies.

### (c) How many copies should be sold to break even?
The break-even point occurs when profit is zero:

\[
P(x) = 0.1x - 68 = 0
\]

Solve for $ x $:

\[
0.1x = 68 \implies x = \frac{68}{0.1} = 680
\]

So, 680 copies need to be sold to break even.

### Summary:
- **Cost function**: $ C(x) = 68 + 0.3x $
- **Revenue function**: $ R(x) = 0.4x $
- **Profit function**: $ P(x) = 0.1x - 68 $
- **Profit (or loss) for 300 copies**: Loss of $38
- **Break-even point**: 680 copies

Would you like more details on any part? Here are some follow-up questions for practice:

1. What is the cost for producing 500 copies?
2. What is the revenue for selling 400 copies?
3. How much profit is made from selling 700 copies?
4. If the price per copy is increased to $0.5, what is the new break-even point?
5. What would be the loss if only 200 copies are sold?

**Tip**: Always check the fixed costs and variable costs separately to ensure you correctly set up the functions for profit and revenue analysis.

Your college newspaper, The Collegiate Investigator, has fixed production costs of $68 per edition and marginal printing and distribution costs of $0.3 per copy. The Collegiate Investigator sells for $0.4 per copy. (a) Write down the associated linear cost, revenue, and profit functions. (b) What profit (or loss) results from the sale of 300 copies? (c) How many copies should be sold in order to break even?

Analyze the cost, revenue, and profit functions for The Collegiate Investigator, with fixed costs of $68 and variable costs of $0.3 per copy. Learn how to calculate profit or loss for 300 copies and determine the break-even point at 680 copies.

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