Finding break-even quantity and break-even revenue in terms of constants given

Question

Suppose the cost function associated with a product is C(x) = cx + F dollars and the revenue function is R(x) = sx, where c denotes the unit cost of production, s the unit selling price, F the fixed cost incurred by the firm, and x the level of production and sales. Find the break-even quantity and the break-even revenue in terms of the constants c, s, and F.

Answer 1

The company breaks even when revenue = cost

 

xs = cx + F

 

xs - cx = F

 

x(s - c) = F      So, x = F/(s - c) is the break even quantity

 

Break even revenue = xs = (F/(s - c))s = Fs/(s - c)