The corner points of the feasible region are $A(0,0)$,$B(16,0)$,$C(8,16)$,and $D(0,24)$. The minimum value of the objective function $z = 300x + 190y$ is . . . . . . .

The objective function of an $LP$ problem is . . . . . . .

The feasible region for an $LPP$ is shown in the figure. Let $z=3x-4y$ be the objective function. The maximum value of $z$ is $....$

If a Linear Programming Problem $(L.P.P.)$ has optimum solutions at two consecutive corner points of the feasible region,then the $L.P.P.$ has:

The coordinates of the corner points of the bounded feasible region are $(0, 10)$,$(5, 5)$,$(15, 15)$,and $(0, 20)$. The minimum value of the objective function $z = 3x + 9y$ is . . . . . . .

The corner points of the feasible region determined by the system of linear constraints are $(2, 72)$,$(15, 20)$,and $(40, 15)$. Let $Z = 6x + 3y$ be the objective function. The minimum value of $Z$ occurs at: