Question No $.4$

Major software companies, after years of providing unlimited free telephone technical support for their products, have recently begun to charge for these services $($ typically after an initial start $-$ up period of $90$ ?days $).$ ? Most companies offer two pricing plans. For instance, Lotus Development offers users of their spreadsheet software the option of paying either $($ i $)$ ?$ $2\mathrm{.}00$ ?per minute for telephone support or $($ ii $)$ ?a $ $129$ ?flat charge for a year of unlimited toll $-$ free calls.

a $.$ ?Consider a customer with a yearly demand for service support of $,$ ?where P is the price per minute and Q is the number of minutes of calls made per year. How many calls would this customer make under plan $($ i $)?$ ? How many calls would he make under plan $($ ii $)?$ ? What would be the annual cost to this customer under each plan?

b $.$ ?Which of the two plans will he choose?