Question

A man owns a hot dog stand. He sells 700 hot dogs per month at $3.25 each making the total revenue $2,275. Each hot dog, bun, and condiments costs the man $0.70 and he has fixed costs of $1,800, making his total costs $2,290. Therefore, he realizes a loss of $15 a month.

1. What is his break-even point?
2. At the current sales levels of 700 hot dogs, what price does the man need to charge in order to break even?
3. If the man reduces his variable costs from $0.70 to $0.60 and all else stays constant (i.e. he still has fixed costs of $1,800 and charges $3.25 per hot dog), what is his new break even point?
4. If the man reduces his fixed costs from $1,800 to $1,700 and all else stays constant (i.e. we still have variable costs of $0.70 each nd charge $3.25 per hot dog), what is his new break even point?
5. Which of these two cost reductions lowers his break even point the most?

Answer 1

(1) Let the number of hot dogs made and sold be x

Revenue = 3.25x

Cost = 0.70x + 1800

3.25x = 0.70x + 1800

x = 705.88 (Say 706)

y = 3.25 * 706 = 2294.50

The break-even point is (706, $2294.50)

(2) Let the price charged be p

Revenue = 700p

Cost = 0.70 * 700 + 1800

700p = 0.70 * 700 + 1800

p = $3.27

(3) Let the number of hot dogs made and sold be x

Revenue = 3.25x

Cost = 0.60x + 1800

3.25x = 0.60x + 1800

x = 679.25 (Say 679)

y = 3.25 * 679 = 2206.75

The break-even point is (679, $2206.75)

(4) Let the number of hot dogs made and sold be x

Revenue = 3.25x

Cost = 0.70x + 1700

3.25x = 0.70x + 1700

x = 666.67 (Say 667)

y = 3.25 * 667 = 2167.75

The break-even point is (667, $2167.75)

(5) Reducing the fixed costs from $1800 to $1700 lowers the break-even point the most.