Which of the following prosthetic knees is most able to prev…
Questions
Which оf the fоllоwing prosthetic knees is most аble to prevent а fаll in a patient with a transfemoral amputation?
Yоu hаve been hired tо а new pоsition аs a Google ad revenue optimizer. In this role, you are responsible for determining which ads to show to which user groups. You have three advertisers (Advertiser 1, Advertiser 2, and Advertiser 3). The following is the maximum number of ads each advertiser is requesting to be displayed: Advertiser 1: up to 85 ads Advertiser 2: up to 100 ads Advertiser 3: up to 15 ads The users are grouped into three categories based on their browsing behavior, with the following number of users in each group: Young professionals (YP): 20 users Tech enthusiasts (TE): 50 users Environmentalists (EN): 60 users You can assume that each user sees exactly one ad. The expected click-through rate (the probability that a user will click on an ad) is given by the following table: YP TE EN Advertiser 1 0.1 0.2 0.1 Advertiser 2 0.3 0.05 0.05 Advertiser 3 0.35 0.1 0.25 You are asked to formulate a linear program that would determine how many of each type of ads to show to each user group to maximize the total number of clicks, while ensuring the following: The total number of ads shown to each user group should be exactly equal to the number of users in that group. The total number of ads shown for each advertiser cannot exceed the maximum number of ads they requested. Remark 1: Even though it is tempting, you are not asked to solve this problem in Excel (or to solve it by hand). No points will be awarded for Excel solution. Please only answer the questions asked below. Remark 2: If you need to make any additional assumptions, state them clearly. a) Write down the objective function, decision variables and constraints in words. (3 points) b) Write down the decision variables, objective function and constraints mathematically. (6 points) c) Suppose now that your contract with Advertiser 1 requires that the total number of ads with Advertiser 1 must be at least twice as high as the combined number of ads for the remaining advertisers. How would this change your answer to a) and b)? (2 points) d) Ignore part c). Suppose that Advertiser 3 now wants to you to either show all 15 of their ads to the Young Professionals (YP) group, or to not show any of their ads to any user group. How would this change your answer to a) and b)? (3 points)