Please help!!! Healthy foods sells 50 lb. bags of grapes to the military for $10. a bag. The fixed costs of this operation are $80,000, while the variables costs of the grapes are .10 per pound. What is the break even point in bags?
At .1 per pound, the variable cost per bag is $5. Let n be the number of bags at break-even. So Tota revenue is 10*n. Total costs are 80000+5*n.
Break-even is 10*n = 80000 + 5*n -- use algebra and solve for n.
To find the break-even point in bags, we need to determine the total cost and total revenue at the break-even point.
Let's start by calculating the total cost:
Fixed costs: $80,000
Variable costs per pound: $0.10
Weight per bag: 50 lbs.
Variable costs per bag = Variable costs per pound × Weight per bag
Variable costs per bag = $0.10 × 50 lbs. = $5.00
Total cost per bag = Fixed costs + Variable costs per bag
Total cost per bag = $80,000 + $5.00 = $80,005.00
Now, let's calculate the total revenue per bag:
Selling price per bag = $10.00
To break even, the total revenue needs to cover the total cost, so:
Total cost per bag × Break-even quantity = Total revenue per bag × Break-even quantity
Plugging in the values we have:
$80,005.00 × Break-even quantity = $10.00 × Break-even quantity
Now, divide both sides by the revenue per bag ($10.00):
$80,005.00 = $10.00 × Break-even quantity
$8,000.50 = Break-even quantity
Therefore, the break-even point in bags is approximately 8,000 bags.