Acertain type of paper towel costs $$ \$ .19 $$ to manufacture and sells for $$ \$ .69 $$ per roll. The fixed cost of producing 500,000 is $$ \$ 25,000 $$. (A) How many of the 500,000 rolls must be made before the company breaks even? (B) What is the profit on 500,000 rolls?

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Let's analyze the problem step-by-step to determine both the break-even point and the profit for producing 500,000 rolls of paper towels.

### Given:
- **Variable Cost per Roll (C₋v):** \$0.19
- **Selling Price per Roll (P):** \$0.69
- **Fixed Cost (F):** \$25,000

### (A) Break-Even Point

The break-even point occurs when **Total Revenue** equals **Total Cost**.

1. **Total Revenue (TR):**  
   $$
   TR = P \times Q = 0.69Q
   $$
   
2. **Total Cost (TC):**  
   $$
   TC = F + C_v \times Q = 25,000 + 0.19Q
   $$
   
3. **Setting TR = TC for Break-Even:**
   $$
   0.69Q = 25,000 + 0.19Q
   $$
   
4. **Solving for Q:**
   $$
   0.69Q - 0.19Q = 25,000 \
   0.50Q = 25,000 \
   Q = \frac{25,000}{0.50} = 50,000 \text{ rolls}
   $$
   
**Answer (A):** The company must produce **50,000 rolls** to break even.

---

### (B) Profit on 500,000 Rolls

Profit is calculated as **Total Revenue** minus **Total Cost**.

1. **Total Revenue for 500,000 Rolls:**
   $$
   TR = 0.69 \times 500,000 = \$345,000
   $$
   
2. **Total Cost for 500,000 Rolls:**
   $$
   TC = 25,000 + (0.19 \times 500,000) = 25,000 + 95,000 = \$120,000
   $$
   
3. **Profit:**
   $$
   \text{Profit} = TR - TC = 345,000 - 120,000 = \$225,000
   $$
   
**Answer (B):** The profit on producing **500,000 rolls** is **\$225,000**.

---

### Summary
- **(A)** 50,000 rolls must be produced to break even.
- **(B)** Producing 500,000 rolls yields a profit of \$225,000.
**(A) The company must produce 50,000 rolls to break even.** **(B) Producing 500,000 rolls results in a profit of \$225,000.**

Acertain type of paper towel costs to manufacture
and sells for per roll. The fixed cost of producing
500,000 is . (A) How many of the 500,000 rolls
must be made before the company breaks even?
(B) What is the profit on 500,000 rolls?

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Acertain type of paper towel costs to manufacture and sells for per roll. The fixed cost of producing 500,000 is . (A) How many of the 500,000 rolls must be made before the company breaks even? (B) What is the profit on 500,000 rolls?