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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 ?
  • a)
    more than 2000
  • b)
    less than 2000
  • c)
    less than 1000
  • d)
    more than 1000 and less than 2000
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A company manufactures cassettes. Its cost and revenue functions are C...
Given that: Cost function C (x) = 26,000+30x and revenue function R(x) = 43x
Now for profit P(x), R(x)>C(x)
⇒ 43x > 26000 + 30x
⇒ 43x − 30x > 26000
⇒ 13x > 26000
⇒ x > 2000
Hence, number of cassettes to be manufactured for some profit must be more than 2000.
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Community Answer
A company manufactures cassettes. Its cost and revenue functions are C...
To determine the number of cassettes that must be sold by the company to realize some profit, we need to find the point at which the revenue exceeds the cost.

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

Revenue Function:
R(x) = 43x

To find the break-even point, we need to set the revenue equal to the cost and solve for x:

43x = 26,000 + 30x

Combining like terms:

13x = 26,000

Dividing both sides by 13:

x = 2,000

This means that the company must sell more than 2,000 cassettes to realize any profit.

Therefore, the correct answer is option A) more than 2000.
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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 ?a)more than 2000b)less than 2000c)less than 1000d)more than 1000and less than 2000Correct answer is option 'A'. Can you explain this answer?
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