Mixed integer programming. I have written the following model from the exercise information below (it is question 2 and 3), but am missing some constraints to ensure that the binary variables are 1, when the conditions are upheld. Please help me correct my models.

part 2:

Part 3:

1 if 30 or more houses are build 0 if no houses are build USD = Max Returni . Xi 1 Space, 0.9 105 UsD E 10, 1) Xi 0 and integer 1 0 if 150 or more houses are build otherwise yPS Max(Return, ri) - 1.06 yps i-1 Space, 0.9-105 30 ysD r2 150-yPS USD,UPS E 0, 1) Xi 0 andl integer You work for a construction company that recently acquired 100,000 m2 land for building a new housing district, 10% of this land has to be used for roads and infrastructure, while the remaining area should be covered with single family houses, semi-detached houses (2 households) and apartment buildings (4 households). The different types of houses have different space requirements, but also bring different returns on the market. You can see this data in the following table Building type Return [EUR] Space requirement [m2 Single family house 200,000 Semi-detached house 240,000 Apartment building 800 1000 1200 300,000 For all four tasks below: This is a modelling exercise, you do not need to solve the model. In all tasks, declare and describe all variables and constraints. In case you need additional parameters, such as big-M, please specify a reasonable 1. Formulate an explicit mathematical program for the above mentioned data to optimize the number of buildings 2. Extend your model with the following requirement: If you build semi-detached houses, then there need to be at 3. Extend your model with the following requirement: If there are more than 150 households, you also have to support value based on the data above (including justification). per type while maximizing the return. least 30 of them. the opening of a new primary school with 1,000,000 EUR which lowers your return. 1 if 30 or more houses are build 0 if no houses are build USD = Max Returni . Xi 1 Space, 0.9 105 UsD E 10, 1) Xi 0 and integer 1 0 if 150 or more houses are build otherwise yPS Max(Return, ri) - 1.06 yps i-1 Space, 0.9-105 30 ysD r2 150-yPS USD,UPS E 0, 1) Xi 0 andl integer You work for a construction company that recently acquired 100,000 m2 land for building a new housing district, 10% of this land has to be used for roads and infrastructure, while the remaining area should be covered with single family houses, semi-detached houses (2 households) and apartment buildings (4 households). The different types of houses have different space requirements, but also bring different returns on the market. You can see this data in the following table Building type Return [EUR] Space requirement [m2 Single family house 200,000 Semi-detached house 240,000 Apartment building 800 1000 1200 300,000 For all four tasks below: This is a modelling exercise, you do not need to solve the model. In all tasks, declare and describe all variables and constraints. In case you need additional parameters, such as big-M, please specify a reasonable 1. Formulate an explicit mathematical program for the above mentioned data to optimize the number of buildings 2. Extend your model with the following requirement: If you build semi-detached houses, then there need to be at 3. Extend your model with the following requirement: If there are more than 150 households, you also have to support value based on the data above (including justification). per type while maximizing the return. least 30 of them. the opening of a new primary school with 1,000,000 EUR which lowers your return