Alma has decided to purchase a cell phone with Internet access and must choose a rate plan. The “occasional-user” plan is $0.50/minute, regardless of how many minutes of air time are used. The “frequent-user” plan charges a flat rate of $55/month for 70 minutes of air time plus $0.33/minute for any time over 70 minutes. The “executive” plan charges a flat fee of $75 per month for 100 minutes of air time plus $0.25/minute over 100 minutes. In the interest of simplicity, Alma has decided to go with the occasional-user plan to start with and then upgrade as she sees fit at a later date.
a. How much air time per month would Alma need to use before she upgrades from the occasional-user plan to the frequent-user plan?
b. At what usage rate should she switch from the frequent-user plan to the executive plan?