college algebra word problem

Question

A cell phone factory has a cost of production C(x) = 150x + 40,000

 and a revenue function R(x) = 400x.

 What is the break-even point?

Answer 1

Break even is when C = R

150x + 40,000 = 400x

250x = 40,000

25x = 4,000

x = 4,000/25 = 160

x=160 is when profit = exactly zero, the break even point

the break even point is when you aren't making any profits, but not any losses either. Revenues just cover costs. Total Revenue = Total Costs. It's the point where you start to consider shutting down if losses seem likely, but as long as revenues exceed variable costs, it's worth staying in business, since you're stuck with the fixed costs regardless. Total costs = fixed costs + variable costs. TC = FC + VC. If R>VC, you stay open for business, at least until you can sell everything to avoid the fixed costs.