Question

The study shows that the demand(number of units sold) for a new product is 1100 units per week when priced at R350, and 850 units per week when priced at R400. Let x represent the price of the product and y the demand per week. Assume that the the relationship between the price and demand is linear and that the demand is dependent on the price. The linear equation you could use to predict the demand for other prices, is

Answer 1

Given :

Demand for a new product = 1100 units per week for 350 rs per unit.

Demand for a new product = 850 units per week for 400 rs per unit.

To find :

Linear equation to predict the demand for other prices.

Solution :

We have given two units and their respective price.

The Linear equation has form like this,

y = mx + c,

(equation 1)

where

y = function (Demand per week in this case)

x = Domain of function. ( Price of each product in this case)

c = Intercept,

m = Slope of the line.

We have given two points :

$\bf \: (x_1, y_1) = (350,1100) \\ \bf \: </p><p>(x_2,y_2) = (400,850)$

The formula of Linear equation in case of two points are given is :

$\\ \bf \: y - y_1 = (\frac{y_2 - y_1}{x_2 - x_1})(x - x_1) \:$

(equation 2)

Where

x = Price of each unit.

y = Number of units with respect to the given price.

So putting the values of two points,

$\bf \: (x_1, y_1) = (350,1100) \\ \bf \: </p><p>(x_2,y_2) = (400,850)$

In equation 2,

The linear equation is :

$\\ \bf \: y - 1100 = (\frac{850 - 1100}{400 - 350})(x - 1100) \:$

so,

$\\ \bf \: y - 1100 = (\frac{ - 250}{50})(x - 1100) \:$

$\bf \: y - 1100 = - 5x + 5500$

$\bf \: y = - 5x + 6600$

so,

The required linear equation :

y = -5x +6600

Observing this equation with equation 1,

Slope m = -5

Intercept c = 6600.

so,

answer:

y = -5x + 6600