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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{.}37$ a minute for daytime calls and $$\mathrm{.}16$ a minute for evening calls. Plan B has a charge of $$\mathrm{.}46$ a minute for daytime calls and $$\mathrm{.}14$ a minute for evening calls. Plan C has a flat rate of $$75$ with $300$ minutes of calls allowed per month and a charge of $$\mathrm{.}34$ per minute beyond that, day or evening.

a$.$ Determine the total charge under each plan for this case: $130$ minutes of day calls and $50$ 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$,$$$,76\mathrm{.}10],[$Cost for Plan B$,$$$,86\mathrm{.}80],[$Cost for Plan C$,$$$,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.

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

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