Q$2.$ Consider the optimization problem

$ma{x}_{x_1,x_2},c_1{x}_1+c_2{x}_2$

$s.t.\{\begin{array}{c}{a}_{11}{x}_1+a_{12}{x}_2{b}_1\end{array}$

$a_{21}{x}_1+a_{22}{x}_2{b}_2$

$x_{1}0,x_{2}0$

The estimates and ranges of uncertainty for the parameters are shown in the following table:

$(10$ pts$)$ Solve the problem using the estimates of the parameters. What is the optimal

solution and what is the profit?

$(15$ pts$)$ Use robust optimization to solve this problem using the range of uncertainty. What

is the optimal solution and what is the profit?