Question

The cost and revenue functions of a product are given by c(x) = 20x + 4000 and R(x) = 60x + 2000 respectively where x is the number of items produced and sold. The value of x to earn profit is

• A. >50
• B. >60
• C. >80
• D. >40

Answer 1

The Correct Option is A

 We are given the following:

 - Cost function: \( C(x) = 20x + 4000 \)<br>
 - Revenue function: \( R(x) = 60x + 2000 \)<br>

 To find the value of \( x \) (the number of items) that will give a profit, we need to calculate the profit function. The profit function is the difference between revenue and cost:<br>

 \[
 \text{Profit} = R(x) - C(x)
 \]<br>

 Substituting the given functions:<br><br>

 \[
 \text{Profit} = (60x + 2000) - (20x + 4000)
 \]<br>

 Simplifying:<br>

 \[
 \text{Profit} = 60x + 2000 - 20x - 4000
 \]<br>

 \[
 \text{Profit} = 40x - 2000
 \]<br>

 To earn a profit, the profit must be greater than 0:<br><br>

 \[
 40x - 2000 > 0
 \]<br>

 Solving for \( x \):<br>

 \[
 40x > 2000
 \]

 \[
 x > \frac{2000}{40}
 \]

 \[
 x > 50
 \]<br>

 Therefore, the value of \( x \) to earn a profit is greater than 50.<br>

The correct answer is (A) : >50