Question

The owner of a milk store finds that he can sell $980$ liters of milk each week at Rs. $14$ per lit. and $1220$ liters of milk each week at Rs. $16$ per lit. Assuming a liner relationship between selling price and demand , how many liters could you sell weakly at Rs. $17$ per liter?

Answer 1

Suppose that,

Selling price P be along X –axis.

And demand of milk D be along Y-axis.

Let y liter milk be sold at Rs x litre.

Consider the given,

Owner sells 980 litre milk at rs 14/litre.

I.e.$x_1=14,y_1=980$

And owner sells 1220 litre milk at Rs 16/litre.

i.e.

$x_2=16,y_2=1220$

Equation of line passing through $(14,980)and(16,122)$

So,

$(y-980)=\frac{1220-980}{16-14}(x-14)$

$\Rightarrow y-980=\frac{240}{2}(x-14)$

$\Rightarrow y-980=120(x-14)$

$\Rightarrow y=120(x-14)+980$

We need to find y when $x=17$

Putting $x=17$ in (1)

$y=120(x-14)+980$

$y=120(17-14)+980$

$y=120\times 3+980$

$y=360+980$

$y=1340$

Hence, 1340 like milk may be sold at Rs 17/litre.