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1. A phone customer is deciding between two long-distance plans. Plan 1 chares 99c for the first 20 minutes, and 10¢ per minute thereafter. Plan 2 charges 10c per minute. (Any fractions of a minute are charged proportionally in each plan.) The time X that the customer spends on a phone call is exponentially distributed, with an average time of 10 minutes. a) What is the cost function h, (X) for plan 1? b) What is the expected cost for plan 1? c) What is the cost function h2(X) for plan 2? d) What is the expected cost for plan 2?

1. A phone customer is deciding between two long-distance plans. Plan 1 chares 99c for the first 20 minutes, and 10¢ per minute thereafter. Plan 2 charges 10c per minute. (Any fractions of a minute are charged proportionally in each plan.) The time X that the customer spends on a phone call is exponentially distributed, with an average time of 10 minutes. a) What is the cost function h, (X) for plan 1? b) What is the expected cost for plan 1? c) What is the cost function h2(X) for plan 2? d) What is the expected cost for plan 2?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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### Problem Description A phone customer is deciding between two long-distance plans. - **Plan 1** charges $0.99 for the first 20 minutes and $0.10 per minute thereafter. - **Plan 2** charges $0.10 per minute (any fractions of a minute are charged proportionally in each plan). The time \( X \) that the customer spends on a phone call is exponentially distributed, with an average time of 10 minutes. ### Questions a) What is the cost function \( h_1(X) \) for plan 1? b) What is the expected cost for plan 1? c) What is the cost function \( h_2(X) \) for plan 2? d) What is the expected cost for plan 2? ### Solutions #### a) Cost function for Plan 1 - **Expression:** \( h_1(X) = 0.99 + 0.10X \), where \( X > 20 \). - Plan 1 has a base charge of $0.99 for the first 20 minutes. For any minutes beyond 20, an additional $0.10 per minute is added. #### b) Expected cost for Plan 1 - **Result:** About $0.99. - Explanation provided: The expected cost is $0.99, which accounts for the first 20 minutes priced at $0.99. #### c) Cost function for Plan 2 - **Expression:** \( h_2(X) = 0.10X \). - Plan 2 charges a straightforward rate of $0.10 per minute, with no initial fixed charge. #### d) Expected cost for Plan 2 - **Result:** About $1. - Explanation: Calculated as \( 0.10 \times 10 = $1 \), based on the average call duration of 10 minutes. ### Diagram Explanation The diagram presents handwritten annotations for each question: - **Plan 1 Equation:** Shows calculation \( 0.99 + 0.10X \). - **Note for Expected Cost (b):** Clarifies that the expected cost for the first 20 minutes is $0.99. - **Plan 2 Equation:** Lists the cost as \( 0.10X \), labeled as the "cost equation." - **Expected Cost for Plan 2:** A calculation box shows \( 0.10
Transcribed Image Text:### Problem Description A phone customer is deciding between two long-distance plans. - **Plan 1** charges $0.99 for the first 20 minutes and $0.10 per minute thereafter. - **Plan 2** charges $0.10 per minute (any fractions of a minute are charged proportionally in each plan). The time \( X \) that the customer spends on a phone call is exponentially distributed, with an average time of 10 minutes. ### Questions a) What is the cost function \( h_1(X) \) for plan 1? b) What is the expected cost for plan 1? c) What is the cost function \( h_2(X) \) for plan 2? d) What is the expected cost for plan 2? ### Solutions #### a) Cost function for Plan 1 - **Expression:** \( h_1(X) = 0.99 + 0.10X \), where \( X > 20 \). - Plan 1 has a base charge of $0.99 for the first 20 minutes. For any minutes beyond 20, an additional $0.10 per minute is added. #### b) Expected cost for Plan 1 - **Result:** About $0.99. - Explanation provided: The expected cost is $0.99, which accounts for the first 20 minutes priced at $0.99. #### c) Cost function for Plan 2 - **Expression:** \( h_2(X) = 0.10X \). - Plan 2 charges a straightforward rate of $0.10 per minute, with no initial fixed charge. #### d) Expected cost for Plan 2 - **Result:** About $1. - Explanation: Calculated as \( 0.10 \times 10 = $1 \), based on the average call duration of 10 minutes. ### Diagram Explanation The diagram presents handwritten annotations for each question: - **Plan 1 Equation:** Shows calculation \( 0.99 + 0.10X \). - **Note for Expected Cost (b):** Clarifies that the expected cost for the first 20 minutes is $0.99. - **Plan 2 Equation:** Lists the cost as \( 0.10X \), labeled as the "cost equation." - **Expected Cost for Plan 2:** A calculation box shows \( 0.10
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