Profit Function Analysis and Applications

The video tutorial explains how to derive the profit function from given cost and revenue functions for producing designer dog leashes. It demonstrates how to calculate the number of leashes needed to maximize profit using the vertex of a quadratic function. The tutorial also covers how to determine the maximum profit and the optimal price per leash to achieve this profit.

What is the formula for the profit function in terms of revenue and cost?

• Profit = Revenue + Cost

• Profit = Revenue - Cost

• Profit = Cost - Revenue

• Profit = Revenue x Cost

What is the simplified form of the profit function P(x) given in the video?

• P(x) = 2x^2 - 52x + 10

• P(x) = -2x^2 + 59x + 10

• P(x) = 2x^2 + 52x - 10

• P(x) = -2x^2 + 52x - 10

How many dog leashes need to be sold to achieve maximum profit?

• 20 leashes

• 15 leashes

• 13 leashes

• 10 leashes

What is the x-coordinate of the vertex of the profit function's graph?

• 13

• 15

• 12

• 10

What is the maximum profit achieved by selling the optimal number of leashes?

• $328

• $400

• $300

• $350

What is the y-coordinate of the vertex of the profit function's graph?

• 300

• 328

• 350

• 400

What is the role of the vertex in the context of the profit function?

• It determines the minimum cost.

• It determines the maximum profit.

• It determines the maximum cost.

• It determines the minimum profit.

What is the price per leash to maximize the profit?

• $30

• $33

• $35

• $40

What is the expression for the price demand function p(x)?

• p(x) = -2x - 59

• p(x) = -2x + 59

• p(x) = 2x + 59

• p(x) = 2x - 59

How is the revenue function expressed in terms of the price demand function?

• R(x) = p(x) - x

• R(x) = p(x) / x

• R(x) = p(x) + x

• R(x) = p(x) * x