Question

The fixed cost of a product is ₹ 30,000 and its variable cost per unit is ₹ 800. If the demand function is p(x) = 4500 – 100x. Find the break-even values.

Answer 1

Let the number of items be x.

∴ Variable cost = ₹ 800x

and Fixed cost = ₹ 30,000

∴ Cost function

C(x) = Variable cost + Fixed cost

C(x) = 800x + 30000    ...(1)

Given demand function

P(x) = 4500 – 100x

∴ Revenue function

R(x) = x · P(x)

R(x) = 4500x – 100x²   ...(2)

Now at break-even point

R(x) = C(x)

4500x – 100x² = 800x + 30000

100x² – 3700x + 30000 = 0

x² – 37x + 300 = 0

(x – 25)(x – 12) = 0

∴ x = 12 or 25

Hence, break even values are 12 and 25.