Questions: The profit for a product is given by P(x)=16x-5060, where x is the number of units produced and sold. Find the marginal profit for the product. The marginal profit for the product is per unit.

Solution Steps

To find the marginal profit for the product, we need to determine the derivative of the profit function \( P(x) \). The marginal profit is the rate of change of the profit with respect to the number of units produced and sold.

The profit function for the product is given by: \[ P(x) = 16x - 5060 \] where \( x \) is the number of units produced and sold.

The marginal profit is the derivative of the profit function \( P(x) \) with respect to \( x \). We calculate: \[ P'(x) = \frac{d}{dx}(16x - 5060) \]

Differentiating \( P(x) \) with respect to \( x \): \[ P'(x) = 16 \]

Final Answer