A salon sells its cologne wholesale for \( \$ 8.75 \) per bottle. The variable costs of producing \( x \) hundred bottles 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. Which expression represents revenue? \( \begin{array}{ll}\text { A. } R=875 x & \text { B. } R=8750 x \\ \text { C. } R=8.75 x & \text { D. } R=8.75 x+25,000\end{array} \)

To find the expression representing revenue, we first need to determine how revenue is calculated. Revenue \( R \) is found by multiplying the price per bottle by the number of bottles sold. Since the given price is \( \$8.75 \) per bottle and \( x \) represents the number of hundreds of bottles, the revenue can be expressed as: \[ R = 8.75 \times 100 \times x = 875 x. \] Thus, the correct answer for revenue is: **A. \( R=875 x \)** Now, let's talk about the cost and profit expressions. The total cost \( C \) consists of the variable costs and fixed costs. The variable cost function is given as \( C_v = -3x^2 + 348x - 325 \), and adding the fixed costs gives: \[ C = C_v + \text{fixed costs} = (-3x^2 + 348x - 325) + 25000. \] Now, profit \( P \) is calculated as revenue minus cost: \[ P = R - C. \] And voilà! You now have the essential expressions you need for revenue, cost, and profit.