(3) A study on optimizing revenue from a website considered dividing cus- tomers into two groups based on a value r bound between 0 and 1, where r measures the proportion of the total bandwidth requested by a customer. Customers with a request less than z were considered low revenue, and those above z high revenue. The expected revenue from the low revenue customers was described by R(1) = Cr(1 – e-kz), where C and k are positive constants based on attributes of the website and the customers. Source: The journal of the Operational Research Society. (a) Find R'(x) and use it to find for what values of r in [0,1], the rev- enue is increasing. (Hint: (b) R" (1) and use it to find for what values of a in [0,1] the revenue function is concave up

(3) A study on optimizing revenue from a website considered dividing cus- tomers into two groups based on a value r bound between 0 and 1, where r measures the proportion of the total bandwidth requested by a customer. Customers with a request less than z were considered low revenue, and those above z high revenue. The expected revenue from the low revenue customers was described by R(1) = Cr(1 – e-kz), where C and k are positive constants based on attributes of the website and the customers. Source: The journal of the Operational Research Society. (a) Find R'(x) and use it to find for what values of r in [0,1], the rev- enue is increasing. (Hint: (b) R" (1) and use it to find for what values of a in [0,1] the revenue function is concave up

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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