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Economics: Break Even Point! HELP?
Can someone walk me through the mathematics of this?
Its for a college course and i m confused ha.
Thanks!
A plant has a capacity of 4100 hydraulic pumps per month. The fixed cost is $504000
per month. The variable cost is $166 per pump, and sales price is $328 per pump (assume that sales
equal output volume). What is the breakeven point in number of pumps per month? What percentage reduction will occur in the breakeven point if fixed costs were reduced by 18% and unit variable costs by 6%?
1 Answer
- Kathleen KLv 76 years ago
Revenues = R(x) = 328x
Costs = C(x) = 166x + 504000
Breakeven occurs when revenues equal costs (i.e., no profit, no loss):
328x = 166x + 504000
162x = 504000
x ≈ 3111 pumps (which is within the plant's capacity, so all is good).
With an 18% reduction, fixed costs will be $504000*(82%) = $413280
With a 6% reduction, unit variable costs will be $166*(94%) = $156.04
The new cost function after those reductions is C(x) = 156.04x + 413280
New breakeven is 328x = 156.04x + 413280 → x ≈ 2403
From 3111 pumps to 2403 pumps represents a reduction of (3111-2403)/3111 = 22.76%
