A cell phone factory has a cost of production C(x) = 150x + 30,000 and a revenue function R(x) = 400x. What is the break-even point?

120 units of products are required to break even.

Revenue is the amount of money that can be made from selling a particular number of items while cost is the amount of money used to produce those items.

At breakeven point, revenue and cost are the same,

Let x represent the number of units produced. hence at break even:

Revenue = cost

R(x) = C(x)

400x = 150x + 30000

250x = 30000

x = 120 units

Therefore 120 units of products are required to break even.

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Given:

Cost function, C(x) and revenue function, R(x) are

To find:

The break-even point.

Solution:

We know that, at break-even point the cost is equal to revenue.

Equate cost function and revenue function to get the break-even point.

Divide both sides by 250.

Put x=120 in R(x).

It means, the revenue and cost are equal, i.e., 48000 at x=120.

Therefore, the break even point is x=120.