The maximum value of $Z = 4x + 5y$, subject to the constraints $3x + y \leq 15$, $3x + 4y \leq 24$, $x \geq 0$, $y \geq 0$ is

The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of the objective function $Z = 3x + 5y$,subject to the linear constraints given by this system of inequations,is:

The solution set of the inequalities $4x + 3y \leq 60$,$y \geq 2x$,$x \geq 3$,$x, y \geq 0$ is represented by which region?

The objective function $z = 4x + 5y$ subject to the constraints $2x + y \geq 7$,$2x + 3y \leq 15$,$y \leq 3$,$x \geq 0$,and $y \geq 0$ has a minimum value at which point?

Find the point at which the objective function $Z = x + y$ attains its maximum value subject to the constraints $x + 2y \leq 70$, $2x + y \leq 95$, $x \geq 0$, and $y \geq 0$.

The difference between the maximum value and minimum value of the objective function $z = 3x + 5y$ subject to the constraints $x + 3y \leqslant 60$,$x + y \geqslant 10$,$x - y = 0$,and $x, y \geqslant 0$ is: