Problem $12-13$

The function was used to generate following figures in order to illustrate the concept of local optima versus global optima.

Minimize this function using LINGO. If required, round your answers to three decimal places. a$.$ Minimize this function using LINGO. If required, round your answers to three decimal places.

Minimizing this function without the global solver option turned on in LINGO gives $x=$

and $Y=$

for a value of

$.$ This is

minimum.

b$.$ Now minimize this function using LINGO with the Global Solver option turned on$.$ If required, round your answers to three decimal places.

The optimal solution $($which is a

minimum$)$ is $x=$

and $Y=$

of

for and objective function value of

Minimizing this function without the global solver option turned on in LINGO gives X $=$ fill in the blank $1$

and Y $=$ fill in the blank $2$

for a value of

$.$ This is

minimum.

Now minimize this function using LINGO with the Global Solver option turned on$.$ If required, round your answers to three decimal places.

The optimal solution $($which is a

minimum$)$ is X $=$ fill in the blank $6$

and Y $=$ fill in the blank $7$

for and objective function value of fill in the blank $8$