It is known that cost of producing 100 units of a commodity is ₹250 and cost of producing 200 units is ₹300. Assuming that AVC is constant, find the cost function.

$C(x)=200+\frac{1}{2}x$

The correct answer is Option (2) → $C(x)=200+\frac{1}{2}x$

Let the total fixed cost TFC be a.

Let AVC constant = b

Then $TVC = (AVC) x = bx$

$∴ TC= TFC + TVC = a + bx$

Given that when $x = 100, TC = ₹250$ and when $x = 200, TC = ₹300$

$∴ a + 100b = 250$   ...(i)

$a + 200b = 300$   ...(ii)

Subtracting (i) from (ii),

$100b=50 ⇒ b=\frac{1}{2}$

Putting this value of b in (i),

$a + 100.\frac{1}{2}=250 ⇒a=200$

Hence, the cost function is $C (x) = 200 +\frac{1}{2}x$