Kim Davis has decided to purchase a cellular phone, but she is unsure about whic
ID: 3202675 • Letter: K
Question
Kim Davis has decided to purchase a cellular phone, but she is unsure about which rate plan to select. The "regular" plan charges a fixed fee of $65 per month for 1100 minutes of airtime plus 0.30 per every additional minute. The "executive" plan charges a fixed fee of $100 per month for 1300 minutes of airtime plus $0.45 per every additional minute. If Kim expects to use the phone for 24 hours per month, which plan should she select? At what level(s) of use would Kim be indifferent between the two plans?Explanation / Answer
a) as 24 hours =24*60 minutes =1440 minutes
here regular plan charges for 1 month =fixed fee +variable charge above 1100 minute
=65+(1440-1100)*0.3 =$167
executive plan charges for 1 month =fixed fee +variable charge above 1300 minute
=100+(1440-1300)*0.45 =$163
hence she should select; executive plan.
b) let at k minutes Kim will be indifferent
hence regular plan cost at k minutes =executive plan cost at k minutes
65+(k-1100)*0.3 =100+(k-1300)*0.45
65+0.3k-330-100 =0.45k-585
0.45k-0.3k =585-330-100+65
0.15k =220
k=220/0.15 =1466.67 minutes
hence at k=1466.67 minutes she will be indifferent.
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