Question

In a factory, the cost of manufacturing $x$ articles is $Rs.20+2x$ and the selling price of $x$ articles is $Rs.(2.5)x$. Draw the graph and determine.
1) Number of articles to be manufactured and sold to reach break-even point (no profit and no loss situation);
2)The profit made when 60 articles are manufactured and sold.

Answer 1

Hint: For solving the question
1) We have to equate the cost of manufacturing$x$article = the selling price of $x$ articles.
2) We have to replace the x by 60.
  For drawing the graph, we should take different values of $x$.

Complete step by step answer:
 Here in this question it is given that
The cost of manufacturing $x$article is$Rs.20+2x$.
 The selling price of $x$ articles is$Rs.(2.5)x$.
For the break-even point(no profit and no loss situation),
The cost of manufacturing$x$article = the selling price of $x$ articles.
$\begin{align}
  & \Rightarrow Rs.20+2x=Rs.\left( 2.5 \right)x \\
 & \Rightarrow 20=(2.5)x-2x \\
 & \Rightarrow 20=(0.5)x \\
 & \Rightarrow x=\dfrac{20}{0.5} \\
 & \Rightarrow x=40
\end{align}$
For $x=40$ the break-even point occurs, that is the cost of manufacturing = the selling price.
The cost of manufacturing when 60 articles are manufactured will be
 $\begin{align}
  & =Rs.20+2(60) \\
 & \Rightarrow Rs.20+120 \\
 & \Rightarrow Rs.140 \\
\end{align}$
The money earned because of selling when 60 articles are sold will be
$\begin{align}
  & \Rightarrow Rs.\left( 2.5 \right)\left( 60 \right) \\
 & \Rightarrow Rs.\left( 150 \right)
\end{align}$
The profit made when 60 articles are manufactured and sold will be
   \[\begin{align}
  & =\text{ }\left( the\text{ }money\text{ }earned\text{ }\text{ }the\text{ }cost\text{ }of\text{ }manufacturing \right)~ \\
 & =\left( Rs.150 \right)-\left( Rs.140 \right) \\
 & \Rightarrow Rs.10 \\
\end{align}\]
 The profit made when 60 articles are manufactured and sold = Rs.10
For drawing the graph,
For the line of cost of manufacturing $Rs.20+2x$

X	$Rs.20+2x$
0	20
40	100
60	140

For the line of money earned by selling the articles $Rs.(2.5)x$

X	$Rs.(2.5)x$
0	0
40	100

.

Note: While solving this question we should take care that the profit occurs only when the cost of manufacturing is less than the money earned by selling the articles and when the cost of manufacturing is greater than the money earned by selling the articles, the loss occurs.