A real estate agent is considering changing her land line phone plan. involve a monthly service charge of $$20.$ Plan A has a cost of $$\mathrm{.}38$ a minute for daytime calls and $$\mathrm{.}17$ a minute for evening calls. Plan $B$ has a charge of $$\mathrm{.}47$ a minute for daytime calls and $$\mathrm{.}14$ a minute for evening calls. Plan $C$ has a flat rate of $$75$ with $275$ minutes of calls allowed per month and a charge of $$\mathrm{.}36$ per minute beyond that, day or evening.

a$.$ Determine the total charge under each plan for this case: $120$ minutes of day calls and $40$ minutes of evening calls in a month. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

$\backslash$table$[[,,],[$Cost for Plan A$,$$$,72\mathrm{.}40],[$Cost for Plan B$,$$$,82\mathrm{.}00],[$Cost for Plan C$,$$$,95\mathrm{.}00]]$

b$.$ If the agent will only use the service for daytime calls, over what range of call minutes will each plan be optimal? $($Round each answer to the nearest whole number. Include the indifference point itself in each answer.$)$

Plan A is optimal from zero to

minutes. Plan $C$ is optimal from

minutes onward.