##### A company manufactures cassettes and its cost and revenue functions for a week are and R = 2x respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?

We have been a week’s data,

Revenue, R = 2x

Where x = number of cassettes produced and sold in a week.

We know that profit is given by,

Profit = Revenue – Cost …(i)

Revenue is the income that a business has from its normal business activities, usually from the sale of goods and services to customers.

A cost is the value of money that has been used up to produce something or deliver a service and hence is not available for use anymore.

And Profit is the gain in the business.

So, it is justified that profit in any business would be measured by the difference in the capital generated by the business and the capital used up in the business.

Profit generated by the company manufacturing cassettes is given by,

Profit = R – C (from (i))

Where, R = Revenue

C = Cost of cassette

Here,

If R < C, then

Profit < 0

There is a loss.

If R = C, then

Profit = 0

There is no profit no loss.

If R > C, then

Profit > 0

There is a profit.

We need to find the number of cassettes sold to make a profit. That is, we need to find x.

So, R > C (to realize a profit)

Substituting values of R and C. We get

x > 300 × 2

x > 600

This means that x must be greater than 600.

Thus, the company must sell more than 600 cassettes to realize a profit.

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