Problem $5$ CL:$15/$Others:$30$

In

general, linear programs are easier to solve and that is why modelers tend to write linear models as long as it is possible. Sometimes a nonlinear program can be converted into a linear program.

Given the following mathematical representation:

Min $e^x+y$

$s.t.e^{x}y$

$,x^{10}x{x}^{up}$

$,y^{10}y{y}^{up}$

$-3-$

ES$604$ Engineering Optimization

Assignment #$1$

Due: $\frac{14}{08}\frac{?}{2024}$ at $03$:$30$ p$.$m$.$

i$)$ How can you represent it in linear terms and still capture all the necessary information to find the solution of the original problem? $($Assume $x$ and $y$ to be greater than zero$)$

ii$)$ Draw a schematic of the original program and the transformed program for $=1,x^{10}=0,x^{up}=1.v^{10}=1.v^{up}=4.$

Please provide a schematic answer and not just theory.