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Cell Service Marisol is new to town and is in the market for cellular phone service. She has settled on Wildcat Cellular, which will give her a free...

Cell Service 
Marisol is new to town and is in the market for cellular phone service.  She has settled on Wildcat Cellular, which will give her a free phone if she signs a one‐year contract.  Wildcat offers several calling plans.  One plan that she is considering is called “Pick Your Minutes”.  Under this plan, she would specify 
a quantity of minutes, say x, per month that she would buy at 5¢ per minute.  Hence, her upfront cost would be $0.05x.  If her usage is less than this quantity x in a given month, she loses the minutes.  If her usage in a month exceeds this quantity x, she would have to pay 40¢ for each extra minute (that is, each minute used beyond x).  For example, if she contracts for x=120 minutes per month and her actual usage is 40 minutes, her total bill is $120  0.05 = $6.00.  However, if actual usage is 130 minutes, her total bill would be 
$120  0.05 + (130 – 120)  0.40 = $10.00.   
The same rates apply whether the call is local or long distance.  Once she signs the contract, she cannot change the number of minutes specified for a year. Marisol estimates that her monthly needs are best approximated by the Normal distribution, with a mean of 250 minutes and a standard deviation of 24 
minutes.  [Hint:  You might think about the problem this way:  if you pick too many minutes then you have “left over inventory” but if you pick too few minutes then you have “lost sales”.] 
 If Marisol chooses the “Pick Your Minutes” plan described above, how many minutes should she contract for? 

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Marisol is new to town and is in the market for cellular phone service. She has settled on Wildcat Cellular
, which will give her a free phone if she signs a one‐year contract. Wildcat offers...

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