Sam is considering starting a healthy life style this year and is looking to join the local gym for the coming 10 months. He can choose between two plans A or B. In Plan A, the gym charges a sign-up fee of $120 and $30 per month, while in Plan B, there is no sign-up fee but the monthly fee is $45. Answer the following and show your analyses
a) Help Sam make a decision on which plan to choose? Show your work
b) After how many months would both plans become indifferent? Show your work
c) Suppose Sam saw a coupon that costs $10 and will give him a discount of $5/month for the first 6 months of being enrolled in Plan B. Should he purchase the coupon? Justify your answer and show your work.