The minimum value of $Z = 3x + y$, subject to the constraints $2x + 3y \leq 6$, $x + y \geq 1$, $x \geq 0$, $y \geq 0$ is....

$A$ toy company manufactures two types of dolls,$A$ and $B$. Market research and available resources have indicated that the combined production level should not exceed $1200$ dolls per week and the demand for dolls of type $B$ is at most half of that for dolls of type $A$. Further,the production level of dolls of type $A$ can exceed three times the production of dolls of type $B$ by at most $600$ units. If the company makes a profit of $Rs. 12$ and $Rs. 16$ per doll respectively on dolls $A$ and $B$,how many of each should be produced weekly in order to maximize the profit?

For the inequalities $x+y \leq 3$,$2x+5y \geq 10$,$x \geq 0$,$y \geq 0$,which of the following points lies in the feasible region?

The objective function $z=x_1+x_2$,subject to $x_1+x_2 \leq 10, -2x_1+3x_2 \leq 15, x_1 \leq 6, x_1, x_2 \geq 0$,has a maximum value at:

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:

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