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?

Answer 1

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 + 30x – 30x < 43x – 30x 

25000 < 13x 

Dividing both the sides by 13 in above equation

\(\frac{25000}{13}< \frac{13{\text{x}}}{13}\)

1923.07 < x 

Thus, we can say that 1923 cassettes must be sold by the company in order to realize some profit.