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?
Solution:
We know that,
Profit = Revenue – cost
Requirement is, profit > 0
According to the question,
Revenue, R(x) = 43 x
Cost, C(x) = 26,000 + 30 x; 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.
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