Maximizing Profit for Ice Cream Cones Sales

What quantity would maximize profit for the sale of ice cream cones, given the sales price and total cost functions provided? The quantity that maximizes profit for the sale of ice cream cones is approximately 0.434 hundred ice cream cones.

Calculating Profit Maximization for Ice Cream Cone Sales

Total Revenue: Total revenue (R(q)) = Sales price per cone * Quantity (q) = $3.25q

Profit Function: Profit (P(q)) = R(q) - C(q) = $3.25q - (0.73q^3 - 0.95q^2 + 3.1q + 0.4)

To find the quantity that maximizes profit, we need to take the derivative of the profit function and set it equal to zero.

Derivative of Profit Function: P'(q) = 3.25 - (2.19q^2 - 1.9q + 3.1) = 0

Solving the equation using the quadratic formula gives us q ≈ 0.434.

Therefore, the quantity that maximizes profit for the sale of ice cream cones is approximately 0.434 hundred ice cream cones.

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