A consumer is trying to decide between two long-distance callingplans. The first one charges a flat rate of $0.10 per minute,whereas the second charges a flat rate of $0.99 for calls up to 20minutes in duration and then $0.10 for each additional minuteexceeding 20 (assume that calls lasting a noninteger number ofminutes are charged proportionately to a whole-minute'scharge). Suppose the consumer's distribution of call durationis exponential with parameter λ. Which plan is better if expected call duration is 10 minutes? 15minutes? [Hint: Let h1(x) denote the cost for the firstplan when call duration is x minutes and let h2(x) bethe cost function for the second plan. Give expressions forthese two cost functions, and then determine the expected cost foreach plan.
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Answer:
(A) The second plan is better plan .
B) The second plan is better plan .
Step-by-step explanation:
Given as :
First phone charge
Flat rate = $0.10 per min
Second phone charge
Flat charge = $0.99 for 20 min
Additional charge = $0.10 for above 20 min
According to question
(a) The call duration = 10 min
Now, for First phone charge
call rate = $0.10 per min × 10 min
∴ call rate = $ 1
Now, for second phone charge
Flat rate = $0.99 for first 20 min
Since call duration is for 10 min
∴ Call rate = $ 0.99
Hence, The second plan is better plan . Answer
(b) (a) The call duration = 15 min
Now, for First phone charge
call rate = $0.10 per min × 15 min
∴ call rate = $ 1.5
Now, for second phone charge
Flat rate = $0.99 for first 20 min
Since call duration is for 15 min
∴ Call rate = $ 0.99
Hence, The second plan is better plan . Answer
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