Problem 8-01 (Algorithmic)

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 8X + Y2 + 8Y + 32

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. Round your answers to the nearest whole number. If negative answer is required, enter the minus sign before the number.

Optimal solution is X = ____________________, Y =_______________________ , for an optimal solution value of 0.