Question

The owner of a milk store finds that, he can sell $980$ litres of milk each week at Rs $14$/litre and $1220$ litres of milk each week at Rs $16$/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs $17$/litre

Answer 1

Assuming selling price per litre along the x-axis and demand along the $y$-axis. we have two points $(14,980)$ and $(16,1220)$ in the $XY$ plane that satisfies the linear relationship between the selling price and demand.

Therefore, the linear relationship between selling price per litre and demand is the equation of the line passing through points $(14,980)$ and $(16,1220)$, which is given by,

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

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

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

i.e $y=120(x-4)+980$

when $x=$Rs $17$/litre,

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

$\Rightarrow y=120\cdot 3+980=360+980=1340$

Thus the owner of the milk store could sell $1340$ litres milk weekly at Rs $17$/litre