<PRE><B>Question 1191483</B>
**Cost Function (C(x))**

* Variable cost per bottle: $5
* Fixed costs: $9,500
* Number of bottles manufactured: x

C(x) = (Variable cost per bottle * Number of bottles) + Fixed costs

**C(x) = 5x + 9500**

**Revenue Function (R(x))**

* Selling price per bottle: $10
* Number of bottles sold: x

R(x) = Selling price per bottle * Number of bottles sold

**R(x) = 10x**

**Break-Even Point**

The break-even point is where the cost equals the revenue (C(x) = R(x)).

1. Set the cost function equal to the revenue function:
   5x + 9500 = 10x

2. Solve for x:
   9500 = 5x
   x = 1900

3. Calculate the cost/revenue at this point:
   C(1900) = 5 * 1900 + 9500 = $19,000
   R(1900) = 10 * 1900 = $19,000

**Interpretation**

**When 1900 water bottles are sold, the cost and revenue both equal $19,000.** This means the manufacturer has covered all their costs (both fixed and variable) and has not yet made a profit. Any bottles sold beyond 1900 will generate profit.
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