Ice Cream Cones: Maximizing Profit Calculation

What quantity would maximize profit for the sale of ice cream cones?

Notice the units of your answer will be "hundreds of ice cream cones". You should enter in the box below your answer from the problem in "hundreds of ice cream cones". So, if the answer is 124 hundres ice cream cones, you will answer 1.24.

Answer:

The quantities that would maximize profit for the sale of ice cream cones are approximately 0.00156 hundred ice cream cones and 0.00334 hundred ice cream cones.

To find the quantity that would maximize profit for the sale of ice cream cones, we need to determine the quantity at which the profit is the highest. Profit is calculated by subtracting the total cost from the total revenue.

First, let's find the revenue function. The revenue is equal to the sales price multiplied by the quantity sold. In this case, the sales price is $2.98 per cone. Therefore, the revenue function can be expressed as: R(q) = 2.98q.

Next, we can find the profit function by subtracting the cost function from the revenue function. The cost function is given as: C(q) = 1.47q^3 - 0.95q^2 + 2.3q + 0.6. Therefore, the profit function is: P(q) = R(q) - C(q).

Now, we can substitute the revenue and cost functions into the profit function. P(q) = 2.98q - (1.47q^3 - 0.95q^2 + 2.3q + 0.6).

To maximize the profit, we need to find the quantity at which the derivative of the profit function is equal to zero. Let's find the derivative of the profit function with respect to q and set it equal to zero:

dP(q)/dq = 2.98 - (4.41q^2 - 1.9q + 2.3) = 0

After solving, we get two possible values for q: q ≈ 0.156 and q ≈ 0.334.