The maximum value of $z$ in the following equation $z=6xy+y^2$,subject to the constraints $3x+4y \leq 100$,$4x+3y \leq 75$,$x \geq 0$,and $y \geq 0$ is:

In the following figure, the shaded region represents the system of constraints:

$A$ wholesale merchant wants to start a cereal business with $Rs \ 24000$. Wheat costs $Rs \ 400$ per quintal and rice costs $Rs \ 600$ per quintal. He has a storage capacity of $200$ quintals of cereal. He earns a profit of $Rs \ 25$ per quintal on wheat and $Rs \ 40$ per quintal on rice. If he stores $x$ quintals of rice and $y$ quintals of wheat,then for maximum profit,the objective function is:

The maximum value of the objective function $z=4x+6y$ subject to the constraints $3x+2y \leq 12$,$x+y \geq 4$,$x, y \geq 0$ 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 $....$

The point at which the maximum value of $Z = x + y$ subject to the constraints $x + 2y \leq 70$, $2x + y \leq 95$, $x \geq 0$, $y \geq 0$ occurs is: