Question 305372
Option 1: $210 set up fee plus $10/inch of the ad.
Option 2: No set up fee but $25/inch of the ad.


Let x equal number of inches of ad space.


Equation for option 1:


C = 210 + 10*x


Equation for option 2:


C = 25*x


b) How many inches of ad space would need to be purchased for option 1 to be less than option 2?


Equation you want to solve is:


210 + 10*x < 25*x


Subtract 10*x from both sides of this equation to get:


210 < 15*x


Divide both sides of this equation by 15 to get:


14 < x


This would be the same as:


x > 14


If the inches of ad space were greater than 14, then option 1 would be cheaper than option 2.


To confirm if this is true, we need to test at x = 13, 14, and 15.


When x = 13, option 1 will cost 210 + 10*13 = 210 + 130 = 340
When x = 14, option 1 will cost 210 + 10*14 = 210 + 140 = 350
When x = 15, option 1 will cost 210 + 10*15 = 210 + 150 = 360


When x = 13, option 2 will cost 25*13 = 325
When x = 14, option 2 will cost 25*14 = 350
When x = 15, option 2 will cost 25*15 = 375 


The results are:


When x = 13, option 1 costs 340 and option 2 costs 325 so option 1 is more expensive than option 2.
When x = 14, option 1 costs 350 and option 2 costs 350 so option 1 and option 2 cost the same.
When x = 15, option 1 costs 360 and option 2 costs 375 so option 1 is cheaper than option 2.


Break even point is when x = 14.


When x > 14, option 1 becomes less than option 2 and stays less than option 2.


Answer to the question is that more than 14 inches of ad space would have to be purchased for option 1 to cost less than option 2.