The maximum value of $Z=10 x+25 y$ subject to $0 \leq x \leq 3, 0 \leq y \leq 3, x+y \leq 5, x \geq 0, y \geq 0$ is

For the $LPP$,minimize $z = x_{1} + x_{2}$ subject to the constraints $5x_{1} + 10x_{2} \geq 0$,$x_{1} + x_{2} \leq 1$,$x_{2} \leq 4$ and $x_{1}, x_{2} \geq 0$.

The solution set of the constraints $2x + 3y \leq 6$,$x + 4y \leq 4$,$x \geq 0$,and $y \geq 0$ includes the point $\ldots$ as a corner point.

There are two factories located at place $P$ and place $Q$. From these locations,a certain commodity is to be delivered to each of the three depots situated at $A, B$ and $C$. The weekly requirements of the depots are $5, 5$ and $4$ units respectively,while the production capacities of the factories at $P$ and $Q$ are $8$ and $6$ units respectively. The cost of transportation per unit is given below:

From/To	$A$	$B$	$C$
$P$	$160$	$100$	$150$
$Q$	$100$	$120$	$100$

How many units should be transported from each factory to each depot in order that the transportation cost is minimum? What will be the minimum transportation cost?

The maximum value of $2x + y$ subject to $3x + 5y \leq 26$ and $5x + 3y \leq 30, x \geq 0, y \geq 0$ is

Corner points of the feasible region for an $\operatorname{LPP}$ are $(0,2), (3,0), (6,0), (6,8)$ and $(0,5)$. Let $F = 4x + 6y$ be the objective function. The minimum value of $F$ occurs at $....$