The fixed cost of a new product is ₹18000 and the variable cost per unit is ₹550. If the demand function is $p(x) = 4000 - 150x$, find the breakeven values.

$x=8$ and $x=15$

The correct answer is Option (1) → $x=8$ and $x=15$

Let x units of the product be produced and sold.

As the variable cost per units is ₹550, 

∴ the variable cost of producing x units = $₹550x$.

As the fixed cost is ₹18000,

∴ total cost of producing x units, $C(x) = ₹(18000 + 550x)$.

Given demand function is $p(x) = 4000 - 150x$ i.e. the selling price per unit is $₹(4000 – 150x)$.

∴ Total revenue on selling x units,

$R(x)$ = (price per unit) (number of units sold)

$=₹(4000 - 150x) x$.

At breakeven values, $C(x) = R(x)$

$⇒18000 + 550x = (4000 - 150x) x$

$⇒150x^2 - 4000x + 550x + 18000 = 0$

$⇒150x^2 - 3450x + 18000 = 0$

$⇒x^2 - 23x + 120 = 0$

$⇒(x-8) (x - 15) = 0$

$⇒x = 8, 15$.

Hence, the breakeven values are $x = 8$ and $x = 15$.