A well-drilling company finds that its marginal profit, in dollars, from drilling a well that is $\mathrm{x}$ feet deep is given by $P^{\prime}(x)=\sqrt[3]{x}$. Find the company's profit from drilling a well that is 240 feet deep. Round to the nearest cent as needed. A: $\$ 1,491.47$ B. $\$ 1,118.60$ C. $\$ 2,478.71$ D. $\$ 1,988.63$

Step 1 ：The marginal profit is the derivative of the profit function. To find the total profit, we need to integrate the marginal profit function from 0 to 240 feet.

Step 2 ：Let's denote the marginal profit function as \(P^{\prime}(x)=x^{\frac{1}{3}}\).

Step 3 ：The total profit is then given by the integral of the marginal profit function from 0 to 240, which is \(P(x) = \int_{0}^{240} P^{\prime}(x) dx\).

Step 4 ：By calculating the integral, we find that the total profit is approximately 1118.60.

Step 5 ：Thus, the company's profit from drilling a well that is 240 feet deep is approximately $1118.60.

Step 6 ：Final Answer: \(\boxed{\$ 1,118.60}\)