The maximum value of the objective function $z=2x+3y$ subject to the constraints $x+y \leq 5$,$2x+y \geq 4$,$x \geq 0$,and $y \geq 0$ is

The minimum value of the objective function $Z = 5x + 8y$,subject to the constraints $x + y \geq 5$,$x \leq 4$,$y \leq 2$,$x \geq 0$,and $y \geq 0$,occurs at the point:

The minimum value of $z = 10x + 25y$ subject to the constraints $0 \leq x \leq 3$,$0 \leq y \leq 3$,and $x + y \geq 5$ is:

The minimum value of $z = 2x + 4y$ subject to constraints $x + 2y \geq 10$,$3x + y \geq 10$,$x \geq 0$,$y \geq 0$ is $....$

Maximum value of $Z=100 x+70 y$ subject to $2 x \geq 4, y \leq 3, x+y \leq 8, x, y \geq 0$ is

The shaded area in the figure below is the solution set for a certain linear programming problem. The linear constraints are given by: