Question:
A company manufactures cassettes. Its cost and revenue function are C(x) = 25000 + 30x and R(x) = 43x respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?
Solution:
Given:
Cost function C(x) = 25000 + 30x
Revenue function R(x) = 43x
To Find:
Number of cassettes to be sold to realize some profit
In order, to gain profit: R(x) > C(x)
Therefore,
43x > 25000 + 30x
25000 + 30x < 43x
Subtracting 30x from both the sides in above equation
$25000+30 x-30 x<43 x-30 x$
$25000<13 x$
Dividing both the sides by 13 in above equation
$\frac{25000}{13}<\frac{13 x}{13}$
$1923.07 Thus, we can say that 1923 cassettes must be sold by the company in order to realize some profit.