A small fast-food restaurant invests $4,000 to produce a new food item that will sell for $4.59. Each item can be produced for $2.19.
(a) How many items must be sold to break even?
(Round your answer to the nearest whole number.)
items
(b) How many items must be sold to make a profit of $5,500? (Round your answer to the nearest whole number.
items
To find the number of items that must be sold to break even, we need to determine the break-even point. The break-even point is reached when the revenue equals the cost.
Let's first calculate the cost per item:
Cost per item = Cost to produce / Number of items
Cost per item = $4,000 / $2.19
Cost per item ≈ $1823.29 (rounded to the nearest cent)
Next, let's calculate the break-even point:
Break-even point = Cost to produce / (Selling price - Cost per item)
Break-even point = $4,000 / ($4.59 - $2.19)
Break-even point ≈ 2072.25 (rounded to the nearest cent)
(a) The number of items that must be sold to break even is approximately 2,072 (rounded to the nearest whole number).
To find the number of items that must be sold to make a profit of $5,500, we need to add the profit amount to the break-even point and calculate based on the new revenue:
Profit point = Break-even point + (Profit / (Selling price - Cost per item))
Profit point = 2,072 + ($5,500 / ($4.59 - $2.19))
Profit point ≈ 4,759.50 (rounded to the nearest cent)
(b) The number of items that must be sold to make a profit of $5,500 is approximately 4,760 (rounded to the nearest whole number).
To find the number of items that must be sold to break even or make a specific profit, we need to use the formula:
Profit or Loss = (Selling Price per Item - Cost per Item) * Number of Items
(a) To break even, the profit should be zero. We can set up the equation:
0 = (4.59 - 2.19) * Number of Items
Solving for the number of items:
Number of Items = 4,000 / (4.59 - 2.19)
Number of Items ≈ 2,237 (rounded to the nearest whole number)
Therefore, to break even, the restaurant must sell approximately 2,237 items.
(b) To make a profit of $5,500, we set up the equation:
5,500 = (4.59 - 2.19) * Number of Items
Solving for the number of items:
Number of Items = 5,500 / (4.59 - 2.19)
Number of Items ≈ 3,607 (rounded to the nearest whole number)
Therefore, to make a profit of $5,500, the restaurant must sell approximately 3,607 items.