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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.
Solution
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.
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