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

The owner sells 980 liters of milk each week at Rs 14/litre and 1220 liters of milk each week at Rs 16/litre . Also the relationship between the selling price and demand is linear.

Since there is a linear relationship between Price/liter and quantity, there is a straight line passes through the points.

Suppose Price/liter is plotted along x- axis and quantity along the y- axis.

The coordinates of the points through which the straight line passes are ( 14,980 ) and ( 16,1220 ) .

Now, the formula for the equation of line passing through the points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by,

( y− y 1 )= y 2 − y 1 x 2 − x 1 ⋅( x− x 1 ) (1)

Substitute ( x 1 , y 1 ) as ( 14,980 ) and ( x 2 , y 2 ) as ( 16,1220 ) in equation (1).

( y−980 )= 1220−980 16−14 ⋅( x−14 ) ( y−980 )= 240 2 ⋅( x−14 ) ( y−980 )=120⋅( x−14 ) y−980=120x−1680

Simplify the above expression.

120x−1680−y+980=0 120x−y−700=0 (2)

Now when the milk price is Rs 17/ litre .

x=17

Substitute the value of x in equation (2).

120⋅17−y−700=0 y=120⋅17−700 =2040−700 =1340 litres

Thus, 1340 litres of milk sell weekly at the rate of Rs 17/ litre