Graphing and Analyzing Break-Even Linear Problems

A local bakery sells cupcakes for $3 each and has a monthly cost of $150. Create a linear equation for the total cost and total revenue. Determine the break-even point and explain its significance in the context of the bakery's operations.

• Total revenue is $150 when 30 cupcakes are sold.

• The bakery's total cost increases with each cupcake sold.

• The break-even point occurs at 25 cupcakes sold.

• The break-even point occurs when total revenue equals total cost, which is at 50 cupcakes sold.

A gym charges a monthly membership fee of $40 and has fixed costs of $500. Write the equations for total revenue and total cost. Graph these equations and identify the break-even point. Discuss what this means for the gym's financial health.

• The gym's fixed costs are $300 instead of $500.

• The total cost is always less than total revenue.

• The gym breaks even at 15 members per month.

• The gym does not have a break-even point with the current pricing and fixed costs.

A lemonade stand has fixed costs of $10 and sells lemonade for $2 per cup. Formulate the equations for total cost and total revenue. Find the break-even point and interpret what it means for the stand's profitability.

• The break-even point is at 5 cups sold.

• The break-even point is at 7 cups sold.

• The break-even point is at 3 cups sold.

• The break-even point is at 10 cups sold.

A concert venue has a fixed cost of $1,000 and sells tickets for $50 each. Write the equations for total revenue and total cost. Graph these equations and find the break-even point. Analyze the implications for the venue's operations.

• The break-even point is at 30 tickets sold.

• The break-even point is at 20 tickets sold.

• The break-even point is at 10 tickets sold.

• The break-even point is at 50 tickets sold.

A subscription box service has a monthly cost of $25 and sells boxes for $40 each. Write the equations for total revenue and total cost. Graph the equations and find the break-even point. Discuss how this affects the service's pricing strategy.

• The total cost equation is TC = 0 + 25x; the total revenue equation is TR = 25x.

• The total cost equation is TC = 25 + 0x; the total revenue equation is TR = 40x. The break-even point occurs at approximately 1 box sold.

• The break-even point occurs at 2 boxes sold.

• The total cost equation is TC = 25x; the total revenue equation is TR = 40 + 0x.

A farmer sells vegetables at a local market for $5 per basket and has fixed costs of $200. Formulate the equations for total revenue and total cost. Identify the break-even point and analyze its importance for the farmer's business.

• The break-even point is 80 baskets.

• The break-even point is 20 baskets.

• The break-even point is 60 baskets.

• The break-even point is 40 baskets.

A tutoring service charges $30 per session and has fixed costs of $600. Write the equations for total revenue and total cost. Graph these equations and find the break-even point. Discuss how this information can guide the service's marketing efforts.

• The break-even point is at 25 sessions.

• The break-even point is at 15 sessions.

• The break-even point is at 30 sessions.

• The break-even point is at 20 sessions.

A mobile app has a subscription fee of $10 per month and fixed costs of $1,200. Create the equations for total revenue and total cost. Determine the break-even point and analyze what this means for the app's sustainability.

• The break-even point is 200 subscribers.

• The break-even point is 100 subscribers.

• The break-even point is 120 subscribers.

• The break-even point is 150 subscribers.