Campus Coffee Cart Break-Even
A student club runs a coffee cart on campus. They pay a one-time permit fee of $180 and a per-day vendor fee of $25 for each day they operate. Each cup costs $1.40 in supplies and sells for $3.75. They plan to operate 12 days this month. On a typical day they sell between 60 and 90 cups, but they are unsure of the exact number and want to know how the numbers behave before committing. The club treasurer wants a clear picture of the break-even point and total profit under different sales assumptions.
1. Write an expression for the club's monthly profit in terms of the total number of cups sold, c, across all 12 days. Then find the minimum number of cups they must sell over the month to break even.
Read the worked answer
Fixed costs: permit $180 plus 12 days × $25/day = $180 + $300 = $480. Variable cost per cup is $1.40, revenue per cup $3.75, so contribution margin per cup = $3.75 − $1.40 = $2.35.
Profit = 2.35c − 480.
Break-even: 2.35c − 480 = 0 → c = 480 / 2.35 ≈ 204.3. Since cups are whole, they need at least 205 cups over the month.
2. If they average 70 cups per day for 12 days, what is the monthly profit? If instead they average 85 cups per day, how much more profit do they make, and why is the increase larger than the extra cups would suggest?
Read the worked answer
At 70/day: c = 840 cups. Profit = 2.35(840) − 480 = 1974 − 480 = $1,494.
At 85/day: c = 1020 cups. Profit = 2.35(1020) − 480 = 2397 − 480 = $1,917.
Difference = $423 for 180 extra cups. Each extra cup adds $2.35 of margin, and 180 × 2.35 = $423. The increase is proportional to extra cups, not to total cups; fixed costs are already covered, so every additional cup contributes its full margin.