Find the break-even point for a firm manufacturing bicycles whose cost function is given as C (x) = 150x + 20,000 and whose revenue function is given as R(x) = 270x.
set C(x) = R(x) ... solve for x
To find the break-even point for a firm, we need to find the value of x where the total cost equals the total revenue.
The cost function for the firm is given as C(x) = 150x + 20,000, where x represents the number of bicycles produced.
The revenue function for the firm is given as R(x) = 270x, where x represents the number of bicycles sold.
At the break-even point, the total cost (C(x)) is equal to the total revenue (R(x)), so we can set up the following equation:
150x + 20,000 = 270x
To solve this equation, we first need to simplify it:
20,000 = 120x
Next, divide both sides of the equation by 120:
20,000/120 = x
166.67 = x
Therefore, the break-even point for the firm manufacturing bicycles is approximately 166.67 bicycles.