A saion sells its cologne wholesale for \( \$ 8.75 \) per bottle. The variable costs of producing \( x \) hundred botties is \( -3 x^{2}+348 x-325 \) dollars, and the fixed costs for manufacturing are \( \$ 25,000 \). Find expressions for the revenue, cost, and profit from selling \( x \) hundred items. 0.33 of 1 Which expression represents revenue? \( \begin{array}{ll}\text { A. } R=875 x & \text { B. } R=8750 x \\ \text { C. } R=8.75 x & \text { D. } R=8.75 x+25,000 \\ \text { Which expression represents cost? } & \text { B. } C=-3 x^{2}+348 x+25,000 \\ \text { A. } C=-3 x^{2}-348 x-24,675 & \text { D. } C=-3 x^{2}+348 x+24,675 \\ \text { C. } C=875 x-25,000 x & \end{array} \)

Let's break down the problem to identify the correct expressions for **revenue** and **cost**. ### Given: - **Selling Price:** \$8.75 per bottle - **Quantity Sold:** \( x \) hundred bottles - **Variable Cost Function:** \( C_{\text{var}}(x) = -3x^2 + 348x - 325 \) dollars - **Fixed Costs:** \$25,000 ### 1. **Revenue (R):** Revenue is calculated as the selling price multiplied by the total number of bottles sold. - **Total Bottles Sold:** Since \( x \) is in hundreds, total bottles = \( 100x \) - **Revenue Formula:** \[ R = \text{Price per Bottle} \times \text{Total Bottles Sold} = 8.75 \times 100x = 875x \] **Correct Option:** - **A. \( R = 875x \)** ### 2. **Cost (C):** Total cost is the sum of variable costs and fixed costs. - **Variable Cost Function:** \( C_{\text{var}}(x) = -3x^2 + 348x - 325 \) - **Fixed Costs:** \$25,000 - **Total Cost Formula:** \[ C = C_{\text{var}}(x) + \text{Fixed Costs} = (-3x^2 + 348x - 325) + 25,000 = -3x^2 + 348x + 24,675 \] **Correct Option:** - **D. \( C = -3x^2 + 348x + 24,675 \)** ### Summary of Correct Choices: - **Revenue:** **A. \( R = 875x \)** - **Cost:** **D. \( C = -3x^2 + 348x + 24,675 \)** If you have any further questions or need clarification on the **profit** expression, feel free to ask!