Maximizing Function Word Problem

The video tutorial explains how to model revenue using polynomials, focusing on a company selling shirts. It covers the impact of price increases on sales and revenue, demonstrating how to create a revenue function. The tutorial includes graphing the function to find maximum revenue and optimal pricing, emphasizing the balance between price and demand.

What is the initial monthly revenue when selling 6000 shirts at $16 each?

• $96,000

• $100,000

• $90,000

• $80,000

How does the number of shirts sold change with each $1 increase in price?

• Increases by 50

• Decreases by 100

• Increases by 100

• Decreases by 50

What happens to revenue when the price is increased by $1, but 100 fewer shirts are sold?

• Revenue doubles

• Revenue increases

• Revenue remains the same

• Revenue decreases

What is the concept of maximum revenue in this context?

• The highest price at which no shirts are sold

• The price point where revenue is highest despite fewer sales

• The price point where expenses are minimized

• The lowest price at which all shirts are sold

What does the variable X represent in the revenue function R(X)?

• The total revenue

• The number of price increases

• The initial price of shirts

• The number of shirts sold

How is the price of shirts modeled in the revenue function?

• 6000 - 100X

• 16 + X

• 16 - 100X

• 6000 + X

What is the optimal number of price increases to maximize revenue?

• 22

• 10

• 30

• 60

What is the maximum revenue achieved according to the graph?

• $130,000

• $144,400

• $120,000

• $150,000

At what price per shirt is the maximum revenue achieved?

• $22

• $60

• $38

• $16

What happens if the price is increased 60 times?

• Sales increase

• No shirts are sold

• Revenue doubles

• Revenue is maximized