The cost of manufacturing x articles is ₹ (50 + 3x). The selling price of x articles is ₹ 4x.

On a graph sheet, with the same axes, and taking suitable scales draw two graphs, first for the cost of manufacturing against no. of articles and the second for the selling price against number of articles.

Use your graph to determine :

(i) No. of articles to be manufactured and sold to breakeven point (no profit and no loss),

(ii) The profit or loss made when

(a) 30

(b) 60 articles are manufactured and sold.

Given:

The cost of manufacturing x articles = ₹ (50 + 3x).

C.P. = ₹ (50 + 3x)

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of C.P.

Let x = 0, then C.P. = ₹ (50 + 3 $\times$ 0) ⇒ C.P. = ₹ 50

Let x = 20, then C.P. = ₹ (50 + 3 $\times$ 20) ⇒ C.P. = ₹ 110

Let x = 40, then C.P. = ₹ (50 + 3 $\times$ 40) ⇒ C.P. = ₹ 170

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

And, the selling price of x articles is ₹ 4x

S.P. = ₹ 4x

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of S.P.

Let x = 0, then S.P. = ₹ 4 $\times$ 0 ⇒ S.P. = ₹ 0

Let x = 20, then S.P. = ₹ 4 $\times$ 20 ⇒ S.P. = ₹ 80

Let x = 40, then S.P. = ₹ 4 $\times$ 40 ⇒ S.P. = ₹ 160

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

(i) The above figure shows the graphs of C.P. and S.P. Since the two straight lines meet at x = 50, it shows that the C.P. of 50 articles is the same as their selling price.

Hence, No. of articles to be manufactured and sold to breakeven point (no profit and no loss) = 0.

(ii)

(a) Draw the vertical line through x = 30, which meets graph for C.P. at ₹ 140 and graph for S.P. at ₹ 120.

C.P. > S.P.

Therefore, loss = C.P. - S.P.

= ₹ 140 - ₹ 120

= ₹ 20

Hence, the loss = ₹ 20.

(b) Draw the vertical line through x = 60, which meets graph for C.P. at ₹ 230 and graph for S.P. at ₹ 240.

C.P. = ₹ 230 and S.P. = ₹ 240

S.P. > C.P.

Therefore, profit = S.P. - C.P.

= ₹ 240 - ₹ 230

= ₹ 10

Hence, the profit = ₹ 10.