The cost of manufacturing $x$ telephones by TATA is given by $C = 3000 + 200 x,$ and the revenue from selling these is $R = 300 x$ . How many telephone must be produced in order to realize a profit.

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Solution

Step 1:
Given data:
Cost of manufacturing $x$ telephones by TATA, $C = 3000 + 200 x$
Revenue, $R = 300 x$
Step 2:
Find the number of telephones that must be produced:
$Total Revenue - Total Cost = Profit$
For the company to make a profit,
$\begin{array}{rcl} Revenue & > & Cost \\ \Rightarrow & 300 x > 3000 + 200 x \\ \Rightarrow & 300 x - 200 x > 3000 [Subtract 200 x on both sides] \\ \Rightarrow & 100 x > 3000 \\ \Rightarrow & x > \frac{3000}{100} [Divide both sides by 100] \\ \Rightarrow & x > 30 \end{array}$
Therefore, $31 or more$ telephones must be produced in order to realize a profit.

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The cost of manufacturingx telephones by TATA is given by C=3000+200x, and the revenue from selling these is R=300x. How many telephone must be produced in order to realize a profit.

The cost of manufacturing $x$ telephones by TATA is given by $C = 3000 + 200 x,$ and the revenue from selling these is $R = 300 x$ . How many telephone must be produced in order to realize a profit.