Question

P(q) = -0.00034q^3 - 0.0782q^2 + 432q - 12000. Use DERIVATIVES (and any necessary algebra) to find the quantity you need to produce and sell to maximize profits.

Answer 1

To maximize profits, take the derivative of the profit function and set it equal to zero. Solve for the value of 'q' that maximizes profits.

Step-by-step explanation:

To find the quantity that maximizes profits, we need to find the value of 'q' that corresponds to the maximum point on the profit function equation P(q) = -0.00034q^3 - 0.0782q^2 + 432q - 12000. We can do this by taking the derivative of the profit function with respect to 'q' and setting it equal to zero.

First, let's find the derivative of the profit function: P'(q) = -0.00034(3q^2) - 0.0782(2q) + 432.

Next, we set the derivative equal to zero and solve for 'q': -0.00034(3q^2) - 0.0782(2q) + 432 = 0.

Finally, we can solve this equation to find the value of 'q' that maximizes profits.