A pizza has a fixed initial cost of $180,000 and a variable cost of $4 for each pizza sold. If the pizza parlor charges $10 for each pizza, how many pizzas will it have to sell before it makes a profit?

Options

A. `24,000`
B. `30,000`
C. `38,000`
D. `42,000`

Answer

To determine how many pizzas the pizza parlor needs to sell to start making a profit, we can follow these steps:

### Step 1: Define the Revenue and Cost
- The revenue from selling \( X \) pizzas is given by:
\[ \text{Revenue} = \text{Price per pizza} \times \text{Number of pizzas sold} = 10X \]
- The total cost consists of a fixed cost and a variable cost. The fixed cost is $180,000 and the variable cost is $4 for each pizza sold. Thus, the total cost is:
\[ \text{Cost} = \text{Fixed Cost} + \text{Variable Cost} = 180,000 + 4X \]

### Step 2: Set Up the Inequality for Profit
- To make a profit, the revenue must be greater than the total cost:
\[ 10X > 180,000 + 4X \]

### Step 3: Solve the Inequality
- Rearranging the inequality:
\[ 10X - 4X > 180,000 \]
\[ 6X > 180,000 \]
- Now, divide both sides by 6:
\[ X > \frac{180,000}{6} \]
\[ X > 30,000 \]

### Conclusion
- Therefore, the pizza parlor must sell more than 30,000 pizzas to start making a profit. Since we are looking for the minimum number of pizzas, the answer is:
\[ X = 30,001 \text{ (at least)} \]