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. Page Views Commitments (in millions) Sports National Total GEICO 2 Delta T-Mobile Capital One Available 6. 5 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. Page Views Commitments (in millions) Sports National Total GEICO 2 Delta T-Mobile Capital One Available 6. 5
