Pens are sold in a local store for 80 cents each. The factory has $1200 in fixed costs plus 5 cents of additional expense for each pen made. Assuming all pens manufactured can be sold, find the break-even point.
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Let's assume the number of pens manufactured and sold is represented by the variable x.
The total cost to manufacture x pens can be calculated using the formula:
Total Cost = Fixed Costs + (Additional Expense per Pen * Number of Pens)
Total Cost = $1200 + ($0.05 * x)
The total revenue from selling x pens can be calculated using the formula:
Total Revenue = Price per Pen * Number of Pens
Total Revenue = $0.80 * x
At the break-even point, the total cost equals the total revenue:
$1200 + ($0.05 * x) = $0.80 * x
Now, let's solve this equation to find the break-even point:
$1200 + $0.05x = $0.80x
$0.75x = $1200
x = $1200 / $0.75
x = 1600
Therefore, the break-even point is 1600 pens.
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