a) Construct an LP model to maximize total contribution.

b) At least 4 hospitals and 3 school must be installed and at most 2 fire station can be installed in the city.

c) A fire station can be placed in any district and is able to handle any adjacent neighborhood.

d) If a fire station is installed in a district a hospital cannot be installed in the same district.

e) If a hospital is installed in a district a school also must be installed in the same district or adjacent neighborhood.

f) All of the option (fire station, hospital, school) cannot be installed in a district simultaneously. Just district 5 must have all of them.

g) For any district and its adjacent neighborhood, total budget must be at most 500$.

h) For any district and its adjacent neighborhood, it must be installed at least 1 school and either a hospital or a fire station.

i) If a hospital is installed in district 5, 2 hospitals and 1 fire station must be installed in its adjacent neighborhoods.

j) What if the contribution of fire station depends on the presence of hospital, how would the objective function change? Consider that contribution of hospital is 10 and the contribution of fire station is 3 when there is a hospital in the district, and 5 when there isnt any hospital in the district. What is the new objective function? Can we establish a linear programming model?

The text part of the question stated in the image above. The questions are specified between a and j. Could you please solve the questions from a to j separately?

Consider the given city is made up of a number of district. The city is reviewing the location of fire stations, hospitals and schools and you are supposed to decide which ones should be installed in which district (for example a school and a fire station should be installed in district 1 and a fire station should be installed in district 2). Contribution of each fire station, hospital and school is 25,50,10 respectively. And setup cost of each fire station, hospital and school is 100,200,80 respectively. Total budget for reviewing is determined as 1600$. For the following options made the necessary change in the model. After question a, all options are independent of each other. You can just write the additional condition. (Each question is Consider the given city is made up of a number of district. The city is reviewing the location of fire stations, hospitals and schools and you are supposed to decide which ones should be installed in which district (for example a school and a fire station should be installed in district 1 and a fire station should be installed in district 2). Contribution of each fire station, hospital and school is 25,50,10 respectively. And setup cost of each fire station, hospital and school is 100,200,80 respectively. Total budget for reviewing is determined as 1600$. For the following options made the necessary change in the model. After question a, all options are independent of each other. You can just write the additional condition. (Each question is