325
The break-even point is expressed as the equation
F + nM <= nP
where
F = Fixed overhead
M = Marginal cost per item
P = Price per item
n = number of items manufactured and sold
So let's figure out the overhead and marginal costs.
Rent of $400,000 per year - Fixed
Admin salaries of $150,000 per year - Fixed
Wood at $400 per play set - Marginal
10 hours of $70 labor per play set - Marginal
Variable overhead costs of $100 per play set - Marginal
Advertising of $100,000 per year - Fixed
Fixed costs:
$400,000 + $150,000 + $100,000 = $650,000
Marginal costs:
$400 + 10 * $70 + $100 = $400 + $700 + $100 = $1,200
Now let's take the formula and solve for n, then plug in the known values and calculate.
F + nM <= nP
F <= nP - nM
F <= n(P - M)
F/(P - M) <= n
$650,000/($3,200 - $1,200) <= n
$650,000/$2,000 <= n
325 <= n
So Homecraft has to produce and sell 325 play sets to break even.
