Corner points of the feasible region determined by the system of linear constraints are $\left(0,3\right), \left(1,1\right)$ and $\left(3,0\right).$ Let $Z=px+qy,$ where $p, q>0.$ Condition on $p$ and $q$ so that the minimum of $Z$ occurs at $\left(3,0\right)$ and $\left(1,1\right)$ is

Linear inequalities for which the shaded region of the given figure is the solution set, are

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

Formulate the $\mathrm{L}.\mathrm{P}.\mathrm{P}.$, so that the units transported from each factory to each depot in such an order that the transportation cost is minimum.