An architectural engineer needs to study the energy efficiencies of at least 1 o

Question

An architectural engineer needs to study the energy efficiencies of at least 1 of 10 large buildings in a certain region. The buildings are numbered sequentially 1,2,..,10. Using decision variables x_i =1, if the study includes building i and = 0 otherwise, write the constraint(s) for each of the following requirements: Only five buildings will be selected for the study. At least one of the first four buildings will be selected. At least two of the last three buildings will be selected. A study must definitely be carried out for building 4. Studies must not be carried out for buildings 2 and 9. Building 10 will be studied only if building 3 is studied.

Explanation / Answer

a) X1+X2+X3.......X10 =5

b) X1+X2+X3+X4 >=1

c) X8+X9+X10>=2
d) X4=1
e)X2+X9=0

f) X3-X10>=0

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