original problem that is referenced in the second problem:

let me know if you need any other information to help solve this problem!

Display Ad Optimization Assume four companies, GEICO, Delta, T-mobile and Capital One, wish to advertise on the Sports and National sections and they contract directly with the newspaper. For each company, the contract specifies the minimum number of times its display ads are shown in these two sections. The contracts sometimes also specify a (minimum) total number of page views that can originate from any section of the newspaper. Page Views Commitments (in millions) Sports National Total GEICO Delta T-Mobile Capital One Available Data Needed for the Model The number of views each section gets per day can be estimated by analyzing historical data. Assume that the Sports section gets six million views per day and the National section get five million views per day. Page Views Commitments (in millions) Sports National Total GEICO Delta T-Mobile Capital One Available Explanation GEICO requires: at least 2 million times per day at Sports section, 1 million times per day at National section. Delta requires: at least 1 million times per day at National section, 2 million times per day combining the Sports and National section. If shows 1.5 million times at Sports, and 1 million times at National, for T-mobile, is this OK? A Yes B No If shows 6 million times at Sports, and 6 million times at National, for T-mobile, is this OK? A Yes B No Page Views Commitments (in millions) Sports National Total GEICO 2 Delta T-Mobile 1 1 Capital One Available M M Structuring the Display Ad Problem Decisions to be made How many times to display each of the Ads? Assumption: only one spot for the Ads. (e.g. cannot show GEICO and Delta ad to one viewer of Sports) Performance measure Total Revenue (due to clicks). Things that restrict your choices --Contract. --Physical constraint: number of viewers. Display Ad Optimization The contract also specifies that The Washington Post receives $2.30 per click-through from each of the four companies. Note: out of 6 million viewers of Sports section per day, some may click the ad of GEICO, some may not. What is the optimal ad placement policy that maximizes the click- through revenues while meeting the contractual obligations? Problem 2. Consider the advertisement display problem discussed in class with the following modifications. Suppose the number of viewers of the Sports section increases from 6 million per day to 8 million per day, and the number of viewers of the National section increases from 5 million per day to 7 million per day. (i) Re-solve the LP, and report which decision variable(s) are changed at the new optimal solution, compared to the previous optimal solution. Remark: No need to report how you re-solve the LP. Only report the changed decision variables. (ii) Target also wants to advertise at the website of Washington Post (WP), so WP signs a new contract with Target, with the following terms: The minimum number of times its display ad is shown in the National section is at least 1 million. There are no other requirements. . For each click of the Target ad in any section, Target will pay WP 2.3 dollars. After some testing, WP finds that the click through rate (CTR) of the Target ad in the Sports section is 3.5%, while the CTR of the Target ad in the National section is 1.5%. Change your spreadsheet to obtain a new LP. Solve the new LP, and report the optimal solution and the optimal value. Remark 1: Again, no need to report how you re-solve the LP. Just report the optimal solution and the optimal value. Remark 2: It is very easy to make a mistake when obtaining the new LP. Make sure you correctly set up the new LP. (iii) Print the sensitivity report you obtain (you can take a screenshot, or directly print by Excel). (iv) In the "Variable Cells" part of the sensitivity report, what is the value of "allowable increase" corresponding to "Target Sports"? What does this mean? Remark: Explain what change will happen if the corresponding objective coefficient increases by an amount that is larger than this "allowable increase". In your explanation, you need to use the specific values (the values depend on the sensitivity report and/or the original table). (v) In the "Constraints" part of the sensitivity report, what does "allowable increase" mean? Explain using any row in the "Constraints" part as an example. Remark: Again, in your explanation, you need to use specific values. (vi) Suppose you are the CEO of WP, and one manager reports two marketing strategies to you. The first can increase 1 million views of the Sports section per day, and the second can increase 1 million views of the National section per day. They cost the same amount of money. Which one do you choose? Why? (vii) What other business insights can you obtain from the reports of Excel? Write at least one thing you can obtain. This should be something that a manager with NO knowledge of linear programming can understand. Display Ad Optimization Assume four companies, GEICO, Delta, T-mobile and Capital One, wish to advertise on the Sports and National sections and they contract directly with the newspaper. For each company, the contract specifies the minimum number of times its display ads are shown in these two sections. The contracts sometimes also specify a (minimum) total number of page views that can originate from any section of the newspaper. Page Views Commitments (in millions) Sports National Total GEICO Delta T-Mobile Capital One Available Data Needed for the Model The number of views each section gets per day can be estimated by analyzing historical data. Assume that the Sports section gets six million views per day and the National section get five million views per day. Page Views Commitments (in millions) Sports National Total GEICO Delta T-Mobile Capital One Available Explanation GEICO requires: at least 2 million times per day at Sports section, 1 million times per day at National section. Delta requires: at least 1 million times per day at National section, 2 million times per day combining the Sports and National section. If shows 1.5 million times at Sports, and 1 million times at National, for T-mobile, is this OK? A Yes B No If shows 6 million times at Sports, and 6 million times at National, for T-mobile, is this OK? A Yes B No Page Views Commitments (in millions) Sports National Total GEICO 2 Delta T-Mobile 1 1 Capital One Available M M Structuring the Display Ad Problem Decisions to be made How many times to display each of the Ads? Assumption: only one spot for the Ads. (e.g. cannot show GEICO and Delta ad to one viewer of Sports) Performance measure Total Revenue (due to clicks). Things that restrict your choices --Contract. --Physical constraint: number of viewers. Display Ad Optimization The contract also specifies that The Washington Post receives $2.30 per click-through from each of the four companies. Note: out of 6 million viewers of Sports section per day, some may click the ad of GEICO, some may not. What is the optimal ad placement policy that maximizes the click- through revenues while meeting the contractual obligations? Problem 2. Consider the advertisement display problem discussed in class with the following modifications. Suppose the number of viewers of the Sports section increases from 6 million per day to 8 million per day, and the number of viewers of the National section increases from 5 million per day to 7 million per day. (i) Re-solve the LP, and report which decision variable(s) are changed at the new optimal solution, compared to the previous optimal solution. Remark: No need to report how you re-solve the LP. Only report the changed decision variables. (ii) Target also wants to advertise at the website of Washington Post (WP), so WP signs a new contract with Target, with the following terms: The minimum number of times its display ad is shown in the National section is at least 1 million. There are no other requirements. . For each click of the Target ad in any section, Target will pay WP 2.3 dollars. After some testing, WP finds that the click through rate (CTR) of the Target ad in the Sports section is 3.5%, while the CTR of the Target ad in the National section is 1.5%. Change your spreadsheet to obtain a new LP. Solve the new LP, and report the optimal solution and the optimal value. Remark 1: Again, no need to report how you re-solve the LP. Just report the optimal solution and the optimal value. Remark 2: It is very easy to make a mistake when obtaining the new LP. Make sure you correctly set up the new LP. (iii) Print the sensitivity report you obtain (you can take a screenshot, or directly print by Excel). (iv) In the "Variable Cells" part of the sensitivity report, what is the value of "allowable increase" corresponding to "Target Sports"? What does this mean? Remark: Explain what change will happen if the corresponding objective coefficient increases by an amount that is larger than this "allowable increase". In your explanation, you need to use the specific values (the values depend on the sensitivity report and/or the original table). (v) In the "Constraints" part of the sensitivity report, what does "allowable increase" mean? Explain using any row in the "Constraints" part as an example. Remark: Again, in your explanation, you need to use specific values. (vi) Suppose you are the CEO of WP, and one manager reports two marketing strategies to you. The first can increase 1 million views of the Sports section per day, and the second can increase 1 million views of the National section per day. They cost the same amount of money. Which one do you choose? Why? (vii) What other business insights can you obtain from the reports of Excel? Write at least one thing you can obtain. This should be something that a manager with NO knowledge of linear programming can understand