# Break-even Problems

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1) Harold operates a hot dog stand at the Jugulars football games. He pays $2000 per game to rent the space. Each hot dog (with bun and condiments) costs him $0.33, and he sells hot dogs for $3 each. If he sells 1200 hot dogs per game, how much profit will he make?

2) Harold (from problem 1) just read about a new hot dog cooker called the Super Dog. With this new cooker, Harold can make and sell twice as many hot dogs. The Super Dog will last only one football season (10 games). How much should Harold be willing to pay for this new machine?

3) Darrel's car just died. It won't start, and it will cost too much to repair. Therefore, Darrell is looking at new cars to purchase. He is considering three different vehicles. The Econo Mile costs $23,000 and gets 34 mpg. The Mid-Sizer costs $20,000 and gets 24 mpg. The Sport Off-road Vehicle costs $18,000 and gets 20 mpg. Darrell drives 10,000 miles per year.

a) If gas costs $3 per gallon, what is the best alternative for Darrell?

b) A new type of gas is being created. It is part oil and part tree bark. It costs half as much as gasoline and doubles the mpg of any vehicle. What is now the best alternative for Darrell?

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Break-even Problems are explored.

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1) Harold operates a hot dog stand at the Jugulars football games. He pays $2000 per game to rent the space. Each hot dog (with bun and condiments) costs him $0.33, and he sells hot dogs for $3 each. If he sells 1200 hot dogs per game, how much profit will he make?

Solution:

Let x be the number of hot dogs

Cost = 2000 + 0.33x

Revenue = 3x

Profit = Revenue - cost = 3x - (2000 + 0.33x) = 2.67x - 2000

Profit of 1200 hotdogs per game = 2.67*1200 - 2000 = $1204

2) Harold (from problem 1) just read about a new hot dog cooker called the Super Dog. With this new cooker, Harold can make and sell twice as many hot dogs. The Super Dog will last only one football season (10 ...

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