KCET · Maths · Basic of Mathematics
The cost and revenue functions of a product are given by \(c(x)=20 x+4000\) and \(R(x)=60 x+2000\) 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 & Solution
Correct Answer
(A) \(>50\)
Step-by-step Solution
Detailed explanation
Given, \(C(x)=20 x+4000\)
\(\begin{aligned}
&R(x)=60 x+2000 \\
&x=\text { number of items produced and sold } \\
&\text { To earn profit, } R(x)-C(x)>0 \\
&\Rightarrow \quad 60 x+2000-20 x-4000>0 \\
&\Rightarrow \quad 40 x-2000>0 \\
&\Rightarrow \quad 40 x>2000 \\
&\Rightarrow \quad x>50
\end{aligned}\)
\(\begin{aligned}
&R(x)=60 x+2000 \\
&x=\text { number of items produced and sold } \\
&\text { To earn profit, } R(x)-C(x)>0 \\
&\Rightarrow \quad 60 x+2000-20 x-4000>0 \\
&\Rightarrow \quad 40 x-2000>0 \\
&\Rightarrow \quad 40 x>2000 \\
&\Rightarrow \quad x>50
\end{aligned}\)
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