A local bakery is considering adding a new line of pies. This will require leasing new equipment at a monthly cost of $6,437. It would cost $4 to produce each new pie, and the expected retail price is $11.How many pies would Old-Fashioned Pies need to see in order to break even on this expansion? (Round up to the nearest integer)
Question
A local bakery is considering adding a new line of pies. This will require leasing new equipment at a monthly cost of 4 to produce each new pie, and the expected retail price is $11.How many pies would Old-Fashioned Pies need to see in order to break even on this expansion? (Round up to the nearest integer)
Solution
To calculate the break-even point, we first need to understand the costs and revenues involved.
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Fixed Costs: The fixed cost here is the monthly lease for the new equipment, which is $6,437.
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Variable Costs: The variable cost is the cost to produce each pie, which is $4.
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Selling Price: The selling price of each pie is $11.
The break-even point is when the total revenue equals the total costs. In this case, the total costs are the fixed costs plus the variable costs (which depend on the number of pies sold), and the total revenue is the selling price times the number of pies sold.
So, we set up the equation:
Total Revenue = Total Costs
which translates to:
(Number of Pies Sold * Selling Price) = Fixed Costs + (Number of Pies Sold * Variable Cost)
Substituting the given values into the equation:
(Number of Pies Sold * 6,437 + (Number of Pies Sold * $4)
Solving this equation for the Number of Pies Sold gives us the break-even point.
First, simplify the equation by subtracting (Number of Pies Sold * $4) from both sides:
(Number of Pies Sold * 4) = $6,437
This simplifies to:
Number of Pies Sold * (4) = $6,437
Which further simplifies to:
Number of Pies Sold * 6,437
Finally, divide both sides by $7 to solve for the Number of Pies Sold:
Number of Pies Sold = 7
This gives us a decimal number. However, since we can't sell a fraction of a pie, we need to round up to the nearest whole number.
So, the bakery would need to sell approximately 920 pies to break even on this expansion.
Similar Questions
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