$6.$ A real estate agent is considering changing her cell phone plan. There are three plans to choose from, all of which involve a weekly service charge of $$20.$ Plan A has a cost of $$0\mathrm{.}45$ a minute for daytime calls and $$0\mathrm{.}20$ a minute for evening calls. Plan B has a charge of S$0\mathrm{.}55$ a minute for day$-$time calls and $$0\mathrm{.}15$ a minute for evening calls. Plan C has a flat rate of $$80$ with $200$ minutes of calls allowed per week and a charge of $$0\mathrm{.}40$ 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 week.

A B C D

$1$ PARTICULARS PLAN A $($$$)$ PLAN B $($$$)$ PLAN C $($$$)$

$2$ MONTHLY SERVICE CHARGE $202020$

$3$ DAY TIME CALL CHARGES $=120*0\mathrm{.}45=120*\mathrm{.}5580$

$4$ NIGHT TIME CHARGES $=40*0\mathrm{.}2=40*0\mathrm{.}150$

$5$ TOTAL $=$SUM$($B$2$:B$4)=$SUM$($C$2$:C$4)=$SUM$($D$2$:D$4)$

Turn around its even worse

b$.$ Prepare a graph that shows total weekly cost for each plan versus daytime call minutes.

c$.$ If the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal?

d$.$ Suppose that the agent expects both daytime and evening calls. At what point $($i$.$e$.,$ percentage of call minutes for daytime calls$)$ would she be indifferent between plans A and B$?$