Question

"Jane Tamlyn paid $225 to rent a carnival booth for four days. She has to decide whether to sell doughnuts or popcorn. Doughnuts cost $1.80 per dozen and can be sold for $3.60 per dozen. Popcorn will require a $113 rental fee for the popcorn maker and $0.08 per bag of pop-corn for the popcorn, butter, salt, and bags; a bag of popcorn could sell for $0.45."

a)Compute the break-even point in dozens of doughnuts if Jane decides to sell doughnuts exclusively and the break-even point in bags of popcorn if she decides to sell popcorn exclusively.
b)Jane estimates that she can sell either 75 doughnuts or 45 bags of popcorn every hour the carnival is open (10 hours a day for four days). Which product should she sell?
c)Jane can sell back to the baker at half cost any doughnuts she fails to sell at the carnival. Unused popcorn must be thrown away. If Jane sells only 70% of her original estimate, which product should she sell? (Assume that she bought or produced just enough to satisfy the demands she originally estimated.)

Answer 1

To sell doughnuts exclusively, Jane would need to sell at least 125 dozens to break even. To sell popcorn exclusively, Jane would need to sell at least 305 bags to break even.

Step-by-step explanation:

To compute the break-even point in dozens of doughnuts if Jane decides to sell doughnuts exclusively, we need to compare the cost of producing the doughnuts to the revenue generated from selling them. The cost of producing a dozen doughnuts is $1.80, and each dozen can be sold for $3.60. Therefore, the break-even point in dozens of doughnuts can be calculated as:

Break-even point = Rental fee / (Selling price - Cost price) = $225 / ($3.60 - $1.80) = $225 / $1.80 = 125 dozens

To compute the break-even point in bags of popcorn if Jane decides to sell popcorn exclusively, we need to compare the cost of producing the popcorn to the revenue generated from selling it. The rental fee for the popcorn maker is $113, and each bag of popcorn can be sold for $0.45. Additionally, the cost per bag for the popcorn, butter, salt, and bags is $0.08. Therefore, the break-even point in bags of popcorn can be calculated as:

Break-even point = Rental fee / (Selling price - Cost price) = $113 / ($0.45 - $0.08) = $113 / $0.37 = 305 bags