A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells

Question

A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising it sells 200 units. For each additional $2000 spent, an additional 20 units are sold.

a) If x is the amount of money that the company spends on advertising, find a formula for y, the number of units sold as a function of x.

b) How many units does the firm sell if it spends $25,000 on advertising?

c) How many units does the firm sell if it spends $50,000 on advertising?

d) How much advertising money must be spent to sell 700 units?



Answer 1

(0, 200) and (2000,220) are points on a line with slope = 20/2000 = 1/100 = (y-200)/x

y = x/100 +200

y(25,000) = 25,000/100+200=250+200= 450

y(50,000) = 50,000/100+200=500+200= 700

$50,000 advertising sells 700

$25,000 advertising sells 450