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:

For the Linear Programming Problem ($L$.$P$.$P$.),maximize $z = 4x_1 + 2x_2$ subject to the constraints $3x_1 + 2x_2 \geq 9$,$x_1 - x_2 \leq 3$,$x_1 \geq 0$,$x_2 \geq 0$,the problem has:

$A$ man rides his motorcycle at the speed of $50 \, km/h$. He has to spend $Rs. \, 2$ per $km$ on petrol. If he rides it at a faster speed of $80 \, km/h$,the petrol cost increases to $Rs. \, 3$ per $km$. He has at most $Rs. \, 120$ to spend on petrol and one hour's time. He wishes to find the maximum distance that he can travel. Express this problem as a linear programming problem.

The maximum value of $z = 3x + 5y$ subject to the constraints $3x + 2y \leq 18$,$x \leq 4$,$y \leq 6$,$x, y \geq 0$,is

The feasible region of the $L$.$P$.$P$. (Linear Programming Problem) to maximize $z = 70x + 50y$ subject to the constraints $8x + 5y \leq 60$,$4x + 5y \leq 40$ and $x \geq 0, y \geq 0$ is:

The maximum value of the objective function $Z = 3x + 2y$ for the linear constraints $x + y \leq 7$,$2x + 3y \leq 16$,$x \geq 0$,$y \geq 0$ is