The purpose of this exercise is to provide practice using the LINGO or Excel solvers. Find the values of X and Y that minimize the function

Min X2 - 4X + Y2 + 8Y + 20

Do not assume nonnegativity of the X and Y variables. Recall that by default LINGO assumes nonnegative variables. In order to allow the variables to take on negative values, you can add

    @FREE(X); @FREE(Y);

Alternatively, if you want LINGO to allow for negative values by default, in the LINGO menu select Options and then click General Solver, and then uncheck the Variables assumed nonnegative tab.