Consider the Linear Programming Problem, where the objective function Z =( x +4 y ) needs to be minimized subject to constraints 2 x + y ≥ 1000; x +2…

Consider the Linear Programming Problem, where the objective function $\displaystyle \mathrm{Z}=(\mathrm{x}+4 \mathrm{y})$ needs to be minimized subject to constraints \[\begin{aligned} & 2 \mathrm{x}+\mathrm{y} \geq 1000 \\ & \mathrm{x}+2 \mathrm{y} \geq 800 \\ & \mathrm{x}, \mathrm{y} \geq 0 \end{aligned} \] Draw a neat graph of the feasible region and find the minimum value of Z.