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 $>=0$; B $>=0.$ 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?