this question is pretty confusing in the way that i'm not entirely sure what it wants the answer to be, but i'll do my best.
i used the simple interest formula to come up with the equations, and the formula is I = PRT, (I) being interest, (P) being the amount, (R) being the rate of interest, (T) being the time, in months
b = the balance on the customer's account
c = service charge
t = number of months
if b > 1000, then c = b*.008t
if b </= to 1000, then c = b*.012t
if b < 50, then c = t
if b = 0, then c = 0
it looks really confusing but i'm hoping it's lining up with what you're learning and not completely ?????
i created the restrictions with the inequalities based on the given information of what happens when a balance exceeds 1000, is less than 1000, is less than 50, and is 0.
i used the remainder of the given information in the problem to get the equations -- the interest rate for b > 1000 is 0.8%, which is .008, b </= 1000 is .012, and so on. i hope this wasn't too terribly confusing, and let me know if you have any questions about how i came up with the equations!!