The constraints $-x_{1} + x_{2} \leq 1$,$-x_{1} + 3x_{2} \leq 9$,$x_{1}, x_{2} \geq 0$ define:

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

The maximum value of $z=x+y$,subjected to $x+y \leq 10, 5x+3y \geq 15, x \leq 6, x, y \geq 0$,

Reshma wishes to mix two types of food $P$ and $Q$ in such a way that the vitamin contents of the mixture contain at least $8$ $units$ of vitamin $A$ and $11$ $units$ of vitamin $B$. Food $P$ costs Rs $60/kg$ and Food $Q$ costs Rs $80/kg$. Food $P$ contains $3$ $units/kg$ of Vitamin $A$ and $5$ $units/kg$ of Vitamin $B$ while food $Q$ contains $4$ $units/kg$ of Vitamin $A$ and $2$ $units/kg$ of vitamin $B$. Determine the minimum cost of the mixture. Let the mixture contain $x$ kg of food $P$ and $y$ kg of food $Q$. Therefore,$x \geq 0$ and $y \geq 0$. The given information can be compiled in a table as follows:

The maximum value of $z = 9x + 13y$ subject to the constraints $2x + 3y \leq 18$,$2x + y \leq 10$,$x \geq 0$,$y \geq 0$ is:

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?