Question

WidgCo is a company that produces widgets. Their monthly operating costs are $27,619, and it costs them $4 to produce each widget. They sell widgets to distributors for $14 each.

Let P represent WidgCo's monthly profit, and let x represent the number of widgets produced and sold each month. Set up an equation that describes the relationship between P and x.
How many widgets must WidgCo produce and sell each month to break even?

Answer 1

P = 10x - 27619

The company must produce and sell 2762 number of widgets each month to break-even.

Explanation:

Let, x represents the number of widgets produced and sold each month.

So, the total making cost for x widgets is = $(27619 + 4x)

Now, if each widget is sold at $14, then the selling price is $14x.

So, the profit that the company makes by selling x widgets is given by

P = 14x - (27619 + 4x) = 10x - 27619 ........... (1)

Now, for break-even P must be equal to zero.

So, 10x - 27619 = 0

⇒ x = 2761.9 ≈ 2762

Therefore, the company must produce and sell 2762 number of widgets each month to break-even. (Answer)