Maximizing Profit from Selling Price

The video tutorial explains how marketing experts use a linear equation to determine the relationship between the selling price and cost of an item. It describes how to calculate yearly profit and discusses methods to maximize profit by expressing it as a function of selling price. The tutorial further explains the profit function's graph, identifying it as a downward-opening parabola, and demonstrates how to find the optimal selling price using the vertex formula. The optimal selling price is calculated to be $23.33, which maximizes yearly profit.

What is the relationship between the selling price and quantity sold as per the given linear equation?

• q = 30s + 800

• q = -30s + 800

• q = 30s - 800

• q = -30s - 800

If the cost to produce an item is $20, what is the formula for calculating yearly profit?

• Profit = Quantity + Selling Price - Cost

• Profit = Quantity - Selling Price + Cost

• Profit = Quantity x (Selling Price - Cost)

• Profit = Quantity x (Selling Price + Cost)

How can the profit be expressed as a function of selling price?

• By substituting q in terms of s

• By substituting s in terms of q

• By subtracting s from q

• By adding s and q

What happens to the quantity sold if the selling price increases?

• The quantity sold increases

• The quantity sold decreases

• The quantity sold remains the same

• The quantity sold doubles

What is the maximum quantity that can be sold if the selling price is zero?

• 900

• 600

• 700

• 800

What does the graph of the profit function look like?

• A downward opening parabola

• A circle

• A straight line

• An upward opening parabola

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

• It represents the maximum profit point

• It represents no significant point

• It represents the minimum profit point

• It represents the average profit point

What is the effect of a negative coefficient on the quadratic term in the profit equation?

• It makes the parabola a straight line

• It has no effect on the parabola

• It makes the parabola open downwards

• It makes the parabola open upwards

How is the optimal selling price calculated using the vertex formula?

• By using the formula a/b

• By using the formula -b/2a

• By using the formula b/2a

• By using the formula -b/a

What is the optimal selling price that maximizes yearly profit?

• $30.00

• $20.00

• $23.33

• $25.00