Andrew Chilli, a stockbroker, has several recommendations to a client. These recommendations can be found in the table below.

$\backslash$table$[[,,,,],[,,,$amount to be$,$expected$],[$investment$,$investment,company,invested,return$],[,$bond,BC Bonds,$\backslash$table$[[500],[1000]],120],[,$bond,$\backslash$table$[[$Quebec City Bonds$],[$Saskatchewan$]],,],[,$utility,$\backslash$table$[[$Saskatchewan$],[$Electricity$]],350,30],[,$utility,New Brunswick Gas,$490,45],[5,$utility,PEI Electric,$700,75],[6,$regular,Canada Paint Co$.,270,20],[7,$regular,Northern Hotels Co$.,800,90],[8,$regular,Nunavik Art Co$.,400,40]]$

The client agrees to this list but provides several conditions:

no more than $$5000$ can be invested

at least five different investments must be purchased

no more than one type of bond can be purchased

at least two utility stocks must be purchased

at least two regular stocks must be purchased.

Formulate this as a $0-1$ integer linear programming problem, using li for each investment, to help the client maximize expected return.