Question

A firm will break even (no profit and no loss) as long as revenue just equals cost. The value of x (the number of items

produced and sold) where C(x) = R(x) is called the break-even point. Assume that the below table can be expressed as a
linear function.
Find (a) the cost function, (b) the revenue function,
and (e) the profit function.
(d) Find the break-even point and decide whether the
product should be produced, given the restrictions on According to the restriction, no more than 19 units can be sold.
sales.
(a) The cost function is C(x) =

Answer 1

Explanation:

(a)

the cost function is

C(x) = 300 + 20x

(b)

the revenue function is

R(x) = 35x

(e)

the profit function

P(x) = R(x) - C(x) = 35x - 300 - 20x = 15x - 300

(d)

break-even is the point where C(x) and R(x) are equal :

C(x) = R(x)

300 + 20x = 35x

300 = 15x

x = 300/15 = 20

so, the break-even is only achieved when 20 units are produced and sold. and with more than 20 sold units the business would then make a profit.

per our restrictions only max. 19 units can be sold, so, the business will always be in the negative numbers (unless they cheat and sell virtual units that were never produced).

therefore, the product should not be produced at all.