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.
Answer & explanation
Correct answer: option 1
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 = $R(x) - C(x)$
$= 8x - (2x + 24000)$
$=6x-24000$