A company produces a commodity with ₹24000 fixed cost. The variable cost is estimated to be 25% of the total revenue recovered on selling the product at a rate of ₹8 per unit. Find the Profit function.

$6x−24000$

The correct answer is Option (1) → $6x−24000$

Let $x$ units of the product be produced and sold. As the selling price of one unit is ₹8, so the total revenue on selling x units = $₹8x$.

Since the variable cost is 25% of total revenue recovered,

so the variable cost = 25% of $₹8x =₹(\frac{25}{100}×8x)=₹2x$.

Fixed cost of the company is ₹24000.

∴ Cost function (in ₹) = $C(x) = 2x + 24000$.

Revenue function (in ₹) = $R(x) = 8x$.

Profit function = $R(x) - C(x)$

$= 8x - (2x + 24000)$

$=6x-24000$