Question

which expression represents profit? a. $p = 11,000 - 800x$ b. $p = 8000x - 11,000$ c. $p = 351x - 11,000$ d. $p = 11,000 - 351x$

Explanation:

To determine the profit expression, we use the formula: Profit (\(P\)) = Total Revenue - Total Cost. Revenue is typically calculated as (Price per unit) × (Number of units, \(x\)), and Cost includes fixed and variable costs.

Step 1: Recall the Profit Formula

Profit is defined as \( P=\text{Revenue}-\text{Cost} \). Revenue is often a linear function of the number of units \( x \) (e.g., \( \text{Revenue} = \text{Price per unit} \times x \)), and Cost can include a fixed cost and a variable cost (but in the context of these options, we focus on the form of the expression).

Step 2: Analyze the Form of Each Option

• Option A: \( P = 11,000 - 800x \) – This would imply revenue is \( 11,000 \) (a fixed amount) and cost is \( 800x \), but revenue is usually dependent on \( x \) (number of units sold), so this is unlikely for profit (it would be profit only if revenue is fixed and cost is variable, but that's unusual for typical business scenarios where revenue scales with \( x \)).
• Option B: \( P = 8000x - 11,000 \) – Here, revenue is \( 8000x \) (price per unit \( 8000 \), times \( x \) units) and cost is \( 11,000 \) (fixed cost). However, the magnitude of \( 8000x \) is very large, and we need to check against other options.
• Option C: \( P = 351x - 11,000 \) – Revenue is \( 351x \) (price per unit \( 351 \), times \( x \) units) and cost is \( 11,000 \) (fixed cost). This follows the profit formula: \( \text{Profit} = (\text{Price per unit} \times x) - \text{Fixed Cost} \).
• Option D: \( P = 11,000 - 351x \) – This is similar to Option A but with a smaller variable cost coefficient. It implies revenue is fixed at \( 11,000 \) and cost is \( 351x \), which is unusual for profit as revenue should scale with \( x \).

Step 3: Contextualize (Typical Business Scenario)

In most business cases, profit is calculated as (Revenue from selling \( x \) units) minus (Total Cost, which often includes a fixed cost like \( 11,000 \) here). If the price per unit is \( 351 \), then revenue is \( 351x \), and if fixed cost is \( 11,000 \), then profit is \( 351x - 11,000 \), which matches Option C. Wait, but let's re - evaluate. Wait, maybe there was a mis - check. Wait, no – let's think again. Wait, maybe the original problem (not fully shown here) has a price per unit of \( 351 \) and fixed cost \( 11,000 \). So profit is revenue (\( 351x \)) minus cost (\( 11,000 \) fixed cost, assuming variable cost is zero or included in the revenue - cost structure). So the correct form is \( P=\text{Revenue}-\text{Cost} \), where revenue is \( 351x \) and cost is \( 11,000 \), so \( P = 351x - 11,000 \), which is Option C. Wait, but maybe I made a mistake earlier. Wait, let's check the options again.

Wait, perhaps the price per unit is \( 351 \), so revenue is \( 351x \), and fixed cost is \( 11,000 \). Then profit is \( 351x - 11,000 \), which is Option C. The other options: Option A and D have revenue as a fixed number minus a variable cost, which is not the typical profit formula (profit should be revenue (variable with \( x \)) minus cost (fixed or variable)). Option B has a very high price per unit (\( 8000 \)) which is less likely unless specified, but Option C with \( 351x - 11,000 \) is the correct form of profit (revenue from selling \( x \) units at \( 351 \) each, minus fixed cost \( 11,000 \)).

Answer:

C. \( P = 351x - 11,000 \)