Profit Function and Parabolas

The video tutorial explains the relationship between the selling price and quantity sold using a linear equation. It discusses how to calculate profit and derives a profit function. The tutorial then demonstrates finding the optimal selling price that maximizes profit using algebraic methods, including completing the square to find the vertex form. The conclusion reveals the optimal selling price and the maximum profit achievable.

What is the relationship between selling price and quantity sold according to the linear equation?

• Selling price and quantity sold are independent.

• As selling price increases, quantity sold decreases.

• As selling price decreases, quantity sold decreases.

• As selling price increases, quantity sold increases.

How is profit per unit calculated?

• Selling price plus production cost

• Production cost minus selling price

• Selling price minus production cost

• Selling price times production cost

What is the expression for profit when quantity is substituted in terms of selling price?

• Negative 30s squared plus 1400s minus 16000

• 30s squared minus 1400s plus 16000

• Negative 30s plus 800

• 30s minus 800

What does a negative coefficient on the s squared term indicate about the parabola?

• The parabola has no vertex.

• The parabola is a straight line.

• The parabola opens downwards.

• The parabola opens upwards.

What is the first step in finding the vertex of the profit function?

• Divide the equation by a constant.

• Multiply the equation by a constant.

• Factor out the negative coefficient.

• Add a constant to the equation.

What is the optimal selling price that maximizes profit?

• $20.00

• $23.33

• $30.00

• $33.00

What is the maximum yearly profit achieved at the optimal selling price?

• $30,000

• $23,000

• $33,000

• $20,000

What happens to the profit function when the expression s minus 70 over 3 squared is zero?

• The profit is minimized.

• The profit is maximized.

• The profit is zero.

• The profit is negative.

How is the expression s minus 70 over 3 squared related to the profit function?

• It is always zero.

• It can be positive or zero.

• It is always negative.

• It is always positive.

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

• It represents the average profit.

• It represents the maximum profit.

• It represents no change in profit.

• It represents the minimum profit.