The function to be maximized is given by $Z=3x+2y$. The feasible region for this function is the shaded region shown in the figure. The linear constraints for this region are given by:

The maximum value of $z=9x+11y$ subject to $3x+2y \leq 12$,$2x+3y \leq 12$,$x \geq 0$,$y \geq 0$ 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 solution set for minimizing the function $z = x + y$ with constraints $x + y \geqslant 2$,$x + 2y \leqslant 8$,$y \leqslant 3$,$x, y \geqslant 0$ contains

$A$ 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?

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?