Question

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.

Answer 1

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