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

Min X$26$X $+$ Y$2+8$Y $+15$

and find the optimal solution value.

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. To allow for negative values in Excel Solver, make sure that the Make Unconstrained Variables Non$-$Negative box is not checked in the Solver Parameters dialog box.

at $($X$,$ Y$)=$