Question

A company manufactures cassettes. Its cost and revenue functions are C(x) = 26,000 + 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 realise some profit?

Answer 1

We know that

Profit = Revenue – cost

Requirement is, profit > 0

According to the question,

Revenue, R(x) = 43x

Cost, C(x) = 26,000 + 30x

Where x is number of cassettes

⇒ Profit = 43x – (26,000 + 30x) > 0

⇒ 13x – 26,000 > 0

⇒ 13x > 26000

⇒ x > 2000

Therefore, the company should sell more than 2000 cassettes to realise profit.