A real estate agent is considering changing her land line phone plan. There are three plans to choose from, all of which involve a monthly service charge of $$20.$ Plan A has a cost of $$\mathrm{.}42$ a minute for daytime calls and $$\mathrm{.}17$ a minute for evening calls. Plan B has a charge of $$\mathrm{.}52$ a minute for daytime calls and $$\mathrm{.}15$ a minute for evening calls. Plan C has a flat rate of $$80$ with $275$ minutes of calls allowed per month and a charge of $$\mathrm{.}38$ per minute beyond that, day or evening.

a$.$ Determine the total charge under each plan for this case: $150$ minutes of day calls and $70$ minutes of evening calls in a month. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Answer is complete and correct.

$\backslash$table$[[,,],[$Cost for Plan A$,$$$,94\mathrm{.}90],[$Cost for Plan B$,$$$,108\mathrm{.}50],[$Cost for Plan C$,$$$,100\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.$)$

Answer is not complete.

Plan A is optimal from zero to

minutes. Plan C is optimal from

minutes onward.

c$.$ Suppose that the agent expects both daytime and evening calls. At what point $($i$.$e$.,$ percentage of total call minutes used for daytime calls$)$ would she be indifferent between plans A and $B?($Do not round intermediate calculations. Enter your answer as a percentage rounded to $2$ decimal places. Omit the $"\%"$ sign in your response.$)$

percent daytime minutes