The production level that maximizes profit is approximately 125.
To find the production level that maximizes profit, we need to set the marginal revenue equal to the marginal cost. The marginal revenue (MR) is the derivative of the revenue function, and the marginal cost (MC) is the derivative of the cost function. The profit function (P) is given by subtracting the cost function from the revenue function:

First, let's calculate the revenue function R(x) using the demand function p(x):

Now, calculate the profit function P(x):

Simplify the Profit Function:

The Derivative of the Profit Function P'(x):

Now, let's set P'(x) equal to zero and solve for x:

Using the quadratic formula:

In this case, a=−0.012, b=3.2, and c=−507.

The correct value for x that maximizes profit is approximately 125.