Question

A company sells its product at the rate of Rs. $6$ per unit. The variable costs are estimated to run $25\%$ of the total revenue received. If the fixed costs for the product are Rs. $4500$. Find the break even point.

• A. $1000$
• B. $2000$
• C. $3000$
• D. $3500$

Answer 1

Answer: (A)

$1000$

$\Rightarrow$ Here, price per unit $\left(p\right)=Rs.6$

$\Rightarrow$ Total revenue $R\left(x\right)=p.x=6x$ where $x$ is the number of unit sold.

$\Rightarrow$ Cost function $C\left(x\right)=4500+\frac{25}{100}R\left(x\right)$

$\Rightarrow$ Cost function $C\left(x\right)=4500+\frac{25}{100}\times 6x$

$\Rightarrow$ $C\left(x\right)=4500+\frac{3}{2}x$

$\Rightarrow$ Profit function $P\left(x\right)=R\left(x\right)-C\left(x\right)$

$\Rightarrow$ $P\left(x\right)=6x-(4500+\frac{3}{2}x)$

$\therefore$ $P\left(x\right)=6x-\frac{3}{2}x-4500$

$\Rightarrow$ At break even point $P\left(x\right)=0$

$\Rightarrow$ $6x-\frac{3}{2}x-4500=0$

$\Rightarrow$ $\frac{12x-3x}{2}-4500=0$

$\Rightarrow$ $x=\frac{9000}{9}=1000$

$\Rightarrow$ Hence, $x=1000$ is break even point.