Question

A company manufactures cassettes and its cost and revenue functions for a week are C = $300 + \dfrac{3}{2}x$ and R = 2x respectively, where x is the number of cassettes produced and sold a week. How many cassettes must be sold for the company to realize a profit?

Answer 1

Hint: Before attempting this question one should have prior knowledge of profit, cost and revenue and also remember that for a company to realize a profit revenue should be greater than cost, use this information to approach the solution of the question.

Complete step by step solution:
According to the given information we know that function of cost of manufactures cassettes is C = $300 + \dfrac{3}{2}x$ and the function of revenue of cassettes is R = 2x here in both the functions x represents the number of cassettes produced and sold in a week
As we know that a company to realize a profit amount of revenue should be greater than the cost of manufactured cassettes i.e. for profit = revenue > cost
So applying the functions in the statement we get
2x > $300 + \dfrac{3}{2}x$
$ \Rightarrow $2x – $\dfrac{3}{2}x$ > 300
$ \Rightarrow $$\dfrac{{4x - 3x}}{2}$ > 300
$ \Rightarrow $$\dfrac{x}{2}$ > 300
$ \Rightarrow $x > 2 $ \times $ 300
$ \Rightarrow $x > 600
Thus it means that the number of cassettes produced and sold a week should be more than 600
Hence the numbers of cassettes must be sold for the company to realize a profit will be 601.

Note: In the above solution we used the general information we use in business in real life to get the profit by selling some article same as we did in this problem let’s discuss in detail how we got the answer so at first we got 2 functions given one is of cost and another is of revenue so the general definition of revenue is amount generated including the discounts and deductions in merchandise returned in business, so by the definition we knew that to get profit our revenue of cassettes should be more than the cost of cassettes manufactured and sold a week, so we directly used this statement in the given functions and got the numbers of cassettes by which we will receive profit in selling this article.