The feasible region for a linear program is identified by these constraints: $2$A $-1$B $0$; $-1$A $+1\mathrm{.}5$B $<200$; A z $0$; B $20.$ An optimizing student in the management science class is interested in finding the best feasible solution under TWO different objectives: Objective $1$ maximizes $4$A $+$ B; Objective $2$ minimizes A $+$ B$.$ Which of the following statements is true about this linear program?$(100,300)$ is a feasible point for the LP$.(0,133\mathrm{.}33)$ is a corner point of the LP$.(100,0)$ is a feasible point for the LP$.$ The LP has $4$ corner points.