A cereal company finds that the number of people who will bu

A cereal company finds that the number of people who will buy one of its products in the first month that it is introduced is linearly related to the amount of money it spends on advertising. If it spends $50,000 on advertising, then 100.000 boxes of cereal will be sold, and if it spends $100,000 on advertising, then 200.000 boxes of cereal will be sold. Write an equation that relates the amount A spent on advertising to the number x of boxes the company aims to sell. How much advertising is needed to sell 300.000 boxes of cereal? Interpret the slope. What is an equation describing the relation between the amount A spent on advertising and the number x of boxes the company intends to sell? How much advertising is needed to sell 300.000 boxes of cereal?

Solution

If the compnay spends $50,000 on advertising , 100,000 boxes of cereals are sold

If the compnay spends $100,000 on advertising , 200,000 boxes of cereals are sold

These are two points for a linear equation: ( 100,000, $ 50,000) and ( 200,000 , $100,000)

a) Gen equation : A = ax +b

where, a is slope and b is the constant

a = ( 100,000 -50,000)/( 200,000 - 100,000) =50,000/100,000 = 1/2 = 0.5

A = 0.5x +b .Find b using the point ( 100,000, $ 50,000)

100000 = 50,000*0.5 +b

b = 75000

A = 0.5x + 75000

b) x= 300,000

A = 0.5*300,000 +75000 = $225000

c) slope = 0.5 means that for every $0.5 spent on advertising 1 box of cereal is sold