Question

The total profit (in dollars) from the sale of x cameras is P(x)=12x−0.02x² −1,0000≤x≤600 Evaluate the marginal profit at x=200 and interpret results.

Answer 1

The marginal profit at x = 200 is $4 per camera, meaning that for each additional camera sold at x = 200, the profit will increase by $4. The interpretation of the result is that at x = 200, the profit function is increasing at a rate of $4 per camera.

Step-by-step explanation:

To evaluate the marginal profit at x = 200, we need to find the derivative of the profit function with respect to x. The derivative of P(x) = 12x - 0.02x^2 - 1000 is dP/dx = 12 - 0.04x. Substituting x = 200 into this derivative equation, we get dP/dx = 12 - 0.04 * 200 = 12 - 8 = 4.

The marginal profit at x = 200 is $4 per camera. This means that for each additional camera sold at x = 200, the profit will increase by $4.

Therefore, the interpretation of the result is that at x = 200, the profit function is increasing at a rate of $4 per camera.