A company manufactures cassettes.

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.

 

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