Healthy Foods, Inc., sells 50-pound bags of grapes to the military for $10 a bag.
The fixed costs of this operation are $80,000, while the variable costs of the
grapes are $.10 per pound.
a. What is the break-even point in bags?
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To calculate the break-even point in bags, we need to determine at what quantity of bags the total revenue equals the total costs.
The total revenue can be calculated by multiplying the selling price per bag by the number of bags:
Total Revenue = Selling Price per Bag * Number of Bags
In this case, the selling price per bag is $10 and the number of bags is the quantity we are trying to find.
The total costs comprise both fixed costs and variable costs. The fixed costs do not change regardless of the number of bags sold, whereas the variable costs depend on the amount of grapes sold.
Total Costs = Fixed Costs + (Variable Costs per Bag * Number of Bags)
In this case, the fixed costs are $80,000, and the variable costs per bag (grapes) is $0.10.
Now, we can set up the equation to find the break-even point:
Total Revenue = Total Costs
10 * Number of Bags = 80,000 + (0.10 * Number of Bags)
Now, let's solve this equation to find the break-even point in bags:
10 * Number of Bags - 0.10 * Number of Bags = 80,000
9.90 * Number of Bags = 80,000
Number of Bags = 80,000 / 9.90
Number of Bags ≈ 8,081
Therefore, the break-even point in bags is approximately 8,081.