The feasible region of an $LPP$ is shown in the figure. If $z = 3x + 9y$,then the minimum value of $z$ occurs at

The solution set of the constraints $x+2y \leq 2000$,$x+y \leq 1500$,$y \leq 600$ and $x \geq 0$ does not include the point

The maximum value of $z=50x+15y$ subject to the constraints $x+y \leq 60$,$5x+y \leq 100$,$x \geq 0$,$y \geq 0$ is at the point:

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 maximum value of $Z=5x+4y$,subject to the constraints $y \leq 2x$,$x \leq 2y$,$x+y \leq 3$,$x \geq 0$,$y \geq 0$ is:

$A$ farmer mixes two brands $P$ and $Q$ of cattle feed. Brand $P$,costing $Rs. 250$ per bag,contains $3$ units of nutritional element $A$,$2.5$ units of element $B$ and $2$ units of element $C$. Brand $Q$ costing $Rs. 200$ per bag contains $1.5$ units of nutritional element $A$,$11.25$ units of element $B$,and $3$ units of element $C$. The minimum requirements of nutrients $A$,$B$ and $C$ are $18$ units,$45$ units and $24$ units respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?