Break Even Analysis: Graphing and Interpreting Slope

A local bakery sells cupcakes for $3 each and has fixed costs of $150. Write a system of equations to represent the total revenue and total cost. Find the break-even point and interpret the slope and intercept.

• The break-even point is at 50 cupcakes.

• The break-even point is at 100 cupcakes.

• The break-even point is at 75 cupcakes.

• The break-even point is at 30 cupcakes.

A gym charges a monthly fee of $40 and an additional $5 per class. Write the equations for total cost and total revenue if a member takes x classes in a month. Graph the equations and identify the break-even point.

• Total Cost: C = 50 + 5x; Total Revenue: R = 5x; Break-even point at 2 classes.

• Total Cost: C = 40 + 10x; Total Revenue: R = 10x; Break-even point at 4 classes.

• Total Cost: C = 40 + 5x; Total Revenue: R = 5x; No break-even point based on class fees alone.

• Total Cost: C = 40; Total Revenue: R = 5x; Break-even point at 8 classes.

A company produces t-shirts at a cost of $10 each and sells them for $15 each. Create a system of equations to represent the cost and revenue. Determine the break-even point and explain the meaning of the slope.

• The slope represents the total profit per t-shirt sold.

• The break-even point is at 5 t-shirts sold.

• The break-even point is at 0 t-shirts sold.

• The break-even point is at 10 t-shirts sold.

A concert venue has a fixed cost of $2000 and sells tickets for $50 each. Write the equations for total cost and total revenue. Graph the lines and find the break-even point. What does the y-intercept represent in this context?

• The break-even point is at (40, 2000) and the y-intercept represents the fixed cost of $2000.

• The break-even point is at (50, 2000) and the y-intercept represents total revenue.

• The break-even point is at (30, 1500) and the y-intercept represents the ticket price of $50.

• The break-even point is at (20, 2000) and the y-intercept represents the total number of tickets sold.

A lemonade stand has fixed costs of $20 and sells lemonade for $2 per cup. Write a system of equations for cost and revenue. Find the break-even point and interpret the slope in terms of profit per cup sold.

• The break-even point is 5 cups sold.

• The break-even point is 15 cups sold.

• The break-even point is 20 cups sold.

• The break-even point is 10 cups sold.

A subscription service charges $15 per month and has a setup fee of $30. Write the equations for total cost and total revenue. Graph the lines and identify the break-even point. Explain the significance of the intercepts.

• Total Cost: C = 15m; Total Revenue: R = 30 + 15m; Break-even point: (2, 0)

• Total Cost: C = 15 + 30m; Total Revenue: R = 15m; Break-even point: (30, 0)

• Total Cost: C = 30 + 15m; Total Revenue: R = 15m; Break-even point: (0, 30)

• Total Cost: C = 30m; Total Revenue: R = 15; Break-even point: (0, 15)

A farmer sells apples for $1.50 per pound and has fixed costs of $200. Create a system of equations for cost and revenue. Determine the break-even point and discuss the meaning of the slope in this scenario.

• The break-even point is 200 pounds of apples.

• The break-even point is approximately 133.33 pounds of apples.

• The break-even point is 150 pounds of apples.

• The break-even point is 100 pounds of apples.

A printing company has a fixed cost of $500 and charges $0.10 per page printed. Write the equations for total cost and total revenue. Graph the equations and find the break-even point. What does the y-intercept indicate?

• Total Cost: TC = 500 + 0.05x; Total Revenue: TR = 0.10x; Break-even point is at 1000 pages; y-intercept indicates total costs.

• Total Cost: TC = 500 + 0.10x; Total Revenue: TR = 0.10x; Break-even point does not exist; y-intercept indicates fixed costs of $500.

• Total Cost: TC = 0.10x; Total Revenue: TR = 500 + 0.10x; Break-even point is at $500; y-intercept indicates variable costs.

• Total Cost: TC = 500; Total Revenue: TR = 0.10x; Break-even point is at 500 pages; y-intercept indicates total revenue.

A tutoring service charges $25 per hour and has fixed costs of $100. Write a system of equations for cost and revenue. Graph the lines and find the break-even point. Interpret the slope in terms of earnings per hour.

• The slope represents a loss of $25 per hour.

• The break-even point is at 5 hours, where revenue is $250.

• The break-even point is at 4 hours, where both cost and revenue equal $200.

• The break-even point is at 2 hours, where costs are $150.