Question

At a certain software company, the cost, C of developing and producing a computer software program is related to the number of copies produced $x$ by the equation $C=30,000+2x$. The company’s total revenues, R are related to the number of copies produced $x$ by the equation $R=6x-10,000$. Calculate the number of copies the company just produced, so that the total revenue is equal to the cost.
(a) 5,000
(b) 6,000
(c) 7,500
(d) 9000
(e) 10,000

Answer 1

Hint: Here, we are given that the Cost of producing copies is related to number of copies by the expression $C=30,000+2x$ and revenue generated is also related to number of copies by expression $R=6x-10,000$ . So, we will equate both the expression and find the value of $x$ and the obtained value of $x$ will be our answer to this problem.

Complete step-by-step answer:
In question we are given that in a certain company, the cost of developing and producing a computer software program is related to the number of copies produced $x$ by the equation $C=30,000+2x$. The company’s total revenue generated is related to the number of copies produced $x$ by the equation $R=6x-10,000$. And we are asked to find the number of copies the company just produced in such a way that the total revenue is equal to the total cost. So, it can be showed by expression as,
$R=C$
Where, R is total revenue of product and C is total cost of product.
Now, R can be given by the equation $R=6x-10,000$ ……………..(i)
And C can be given by equation $C=30,000+2x$ ………………..(ii)
On substituting the values of expressions, we will get,
$6x-10,000=30,000+2x$
On solving the expression, we will get,
$6x-2x=30,000+10,000$
$\Rightarrow 4x=40,000$
$\Rightarrow x=\dfrac{40,000}{4}=10,000$
Thus, the number of copies produced by the company is $10,000$.
Hence, option (e) is correct.

Note: Here, it is given that Cost of copies is equal to revenue generated so we used that data to find the value of $x$. But, if it is not given then we have to use the formula of revenue generated per copy is equal to the product of sale of copies and average cost of copies, which can be given as, $\text{Revenue}=\text{sales}\times \text{Average cost of production}$. So, students must understand the question and work accordingly.