Problem 7: SecureCo sells security cameras in a region that contains six cities. The disstances between each pair of cities are provided in the following table. Distance (in miles) City 1 City 2 City 3 City 4 City 5 City 6 City 1 0 48 130 188 68 191 City 2 48 0 95 200 111 280 City 3 130 95 0 105 59 90 City 4 188 200 105 0 70 80 City 5 68 111 59 70 0 120 City 6 191 280 90 80 120 0 The following table contains the forecasted annual sales of security cameras in each city, which depends on whether a service representative is located within 100 miles of the city. City 1 City 2 City 3 City 4 City 5 City 6 Forecasted Cameras Sold Rep. Within 100 No Rep. Within Miles 100 Miles 1900 1500 2000 1500 800 600 900 600 400 200 1300 700 Each security camera sold yields a revenue of $90. Service representatives may be located in any of the six cities and cost $100,000/yr. Part a: Formulate an ILP to maximize SecureCo's annual profits. Part b: Solve the problem using AMPL/CPLEX and report the obtained optimal solution. Include a typed version of your AMPL model file and/or data file and your AMPL session in your submission. Problem 7: SecureCo sells security cameras in a region that contains six cities. The disstances between each pair of cities are provided in the following table. Distance (in miles) City 1 City 2 City 3 City 4 City 5 City 6 City 1 0 48 130 188 68 191 City 2 48 0 95 200 111 280 City 3 130 95 0 105 59 90 City 4 188 200 105 0 70 80 City 5 68 111 59 70 0 120 City 6 191 280 90 80 120 0 The following table contains the forecasted annual sales of security cameras in each city, which depends on whether a service representative is located within 100 miles of the city. City 1 City 2 City 3 City 4 City 5 City 6 Forecasted Cameras Sold Rep. Within 100 No Rep. Within Miles 100 Miles 1900 1500 2000 1500 800 600 900 600 400 200 1300 700 Each security camera sold yields a revenue of $90. Service representatives may be located in any of the six cities and cost $100,000/yr. Part a: Formulate an ILP to maximize SecureCo's annual profits. Part b: Solve the problem using AMPL/CPLEX and report the obtained optimal solution. Include a typed version of your AMPL model file and/or data file and your AMPL session in your submission