Question

Give an example of a linear program in two variables whose feasible region is infinite, but such that there is an optimum solution of bounded cost.

Short answer

Example 1:

$\begin{array}{l}\mathrm{x}\ge 0\\ \mathrm{y}\ge 0\end{array}$

Example 2:

$\begin{array}{l}x\ge 0\\ y\ge 0\\ x-y\le 1\end{array}$

Step-by-step solution

Explain Linear Program

Linear program is used for optimization tasks that has constraints and the optimization criterion as linear functions. A linear program has the set of variables that needs to be assign with the real values to satisfy the linear inequalities and to minimize or maximize a given linear objective function.

Give an example of linear program

Example 1:

Consider two variable$\mathrm{x}$and$y$. The linear program is as follows:

$\begin{array}{l}\mathrm{x}\ge 0\\ \mathrm{y}\ge 0\end{array}$

Operation or requirement for the constraints :

${\min }_{x,y}(x+y)$

The above solution is possible in bounded cost.

Example 2:

Consider the constraints as follows,

$\begin{array}{l}\mathrm{x}\ge 0\\ \mathrm{y}\ge 0\\ \mathrm{x}-\mathrm{y}\le 1\end{array}$

Operation required:

${\max }_{\mathrm{i},\mathrm{j}}(\mathrm{x}-2\mathrm{y})$

Therefore, an example for the linear program of two variables were obtained.